chapters 1 6 and chapter 7 sections 1 4 short …...the graph shows the depreciation of the...
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PrecalculusFall Final ReviewChapters 1-6 and Chapter 7 sections 1-4 Name___________________________________
SHORT ANSWER. Answer the question. SHOW ALLAPPROPRIATE WORK!
Graph the equation using a graphing utility. Use agraphing utility to approximate the intercepts roundedto two decimal places, if necessary. Use the TABLEfeature to help establish the viewing window.
1) 3x - 4y = 56
Find the midpoint of the line segment joining the pointsP1 and P2.
2) P1 = (-0.6 , -0.2); P2 = (-2.4, -1.8 )
Find the center (h, k) and radius r of the circle with thegiven equation.
3) x2 + 18x + 81 + y2 + 4y + 4 = 36
Decide whether or not the points are the vertices of aright triangle.
4) (9, -6), (15, -4), (14, -9)
Solve the equation algebraically. Verify your solutionwith a graphing utility.
5) x2 - 11x + 30 = 0
Graph the equation.6) x2 + (y - 2)2 = 16
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
Solve.7) A vendor has learned that, by pricinghot dogs at $1.25 , sales will reach 79 hot dogsper day. Raising the price to $2.00 will causethe sales to fall to 46 hot dogs per day. Let ybe the number of hot dogs the vendor sells atx dollars each. Write a linear equation thatrelates the number of hot dogs sold per day,y, to the price x.
List the intercepts for the graph of the equation.8) y2 = x + 9
Find the slope of the line containing the two points.9) (-9, 6); (-9, 5)
Graph the equation by plotting points.10) x = y2
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
Find the distance d(P1, P2) between the points P1 and P2.11) P1 = (7, -7); P2 = (3 , -5)
Graph the equation using a graphing utility. Use agraphing utility to approximate the intercepts roundedto two decimal places, if necessary.
12) 3x2 - 5y = 34
1
Find the center (h, k) and radius r of the circle. Graph thecircle.
13) x2 + y2 + 6x + 12y + 36 = 0
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
Write the standard form of the equation of the circle withradius r and center (h, k).
14) r = 2; (h, k) = (0, -2)
Solve.15) A school has just purchased new computer
equipment for $17,000 .00. The graph showsthe depreciation of the equipment over 5years. The point (0, 17,000 ) represents thepurchase price and the point (5, 0) representswhen the equipment will be replaced. Write alinear equation in slope-intercept form thatrelates the value of the equipment, y, to yearsafter purchase x . Use the equation to predictthe value of the equipment after 2 years.
x2.5
y225002000017500150001250010000750050002500
x2.5
y225002000017500150001250010000750050002500
Find the slope and y-intercept of the line.16) 4x - 7y = 1
Find the slope of the line and sketch its graph.17) 3x + 5y = 26
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
Solve.18) When making a telephone call using a calling
card, a call lasting 6 minutes cost $1.95 . Acall lasting 14 minutes cost $3.95 . Let y be thecost of making a call lasting x minutes using acalling card. Write a linear equation thatrelates the cost of a making a call, y, to thetime x.
Plot the point in the xy-plane. Tell in which quadrant oron what axis the point lies.
19) (0, -1)
x-5 5
y
5
-5
x-5 5
y
5
-5
Use a graphing utility to approximate the real solutions,if any, of the equation rounded to two decimal places.
20) x4 - 3x2 + 4x + 15 = 0
Write the equation of a function that has the givencharacteristics.
21) The graph of y = x2, shifted 7 units downward
2
Use a graphing utility to graph the function over theindicated interval and approximate any local maximaand local minima. If necessary, round answers to twodecimal places.
22) f(x) = x3 - 3x2 + 1; (-5, 5)
Graph the function by starting with the graph of thebasic function and then using the techniques of shifting,compressing, stretching, and/or reflecting.
23) f(x) = 14x3
x-5 5
y
5
-5
x-5 5
y
5
-5
The graph of a function f is given. Use the graph toanswer the question.
24) Is f(3) positive or negative?
5
-5 5
-5
Find the average rate of change for the function betweenthe given values.
25) f(x) = x2 + 2x; from 4 to 8
Determine algebraically whether the function is even,odd, or neither.
26) f(x) = 1x2
Answer the question about the given function.
27) Given the function f(x) = x2 + 2x - 4
, list the
x-intercepts, if any, of the graph of f.
The graph of a function is given. Decide whether it iseven, odd, or neither.
28)
x-10 -8 -6 -4 -2 2 4 6 8 10
y108642
-2-4-6-8
-10
x-10 -8 -6 -4 -2 2 4 6 8 10
y108642
-2-4-6-8
-10
Solve the problem.29) It has been determined that the number of
fish f(t) that can be caught in t minutes in acertain pond using a certain bait isf(t) = 0.27t + 1, for t > 10. Find theapproximate number of fish that can becaught if you fish for 20 minutes.
Locate any intercepts of the function.30) f(x) = -3x + 4 if x < 1
4x - 3 if x ≥ 1
For the graph of the function y = f(x), find the absolutemaximum and the absolute minimum, if it exists.
31)
3
MULTIPLE CHOICE. Choose the one alternative thatbest completes the statement or answers the question.
Match the function with the graph that best describesthe situation.
32) The amount of rainfall as a function of time, ifthe rain fell more and more softly.A)
x
y
x
y
B)
x
y
x
y
C)
x
y
x
y
D)
x
y
x
y
SHORT ANSWER. Answer the question. SHOW ALLAPPROPRIATE WORK!
The graph of a function is given. Decide whether it iseven, odd, or neither.
33)
x-10 -8 -6 -4 -2 2 4 6 8 10
y108642
-2-4-6-8
-10
x-10 -8 -6 -4 -2 2 4 6 8 10
y108642
-2-4-6-8
-10
Find the value for the function.
34) Find f(2) when f(x) = x2 - 6x + 1
.
4
MULTIPLE CHOICE. Choose the one alternative thatbest completes the statement or answers the question.
Match the correct function to the graph.35)
x-5 5
y
5
-5
x-5 5
y
5
-5
A) y = |2 - x| B) y = |x + 2|C) y = |1 - x| D) y = x - 2
SHORT ANSWER. Answer the question. SHOW ALLAPPROPRIATE WORK!
The graph of a function is given. Decide whether it iseven, odd, or neither.
36)
x-π
-π2
π2 π
y54321
-1-2-3-4-5
x-π
-π2
π2 π
y54321
-1-2-3-4-5
For the given functions f and g, find the requestedfunction and state its domain.
37) f(x) = 5 - x; g(x) = x - 1Find f ∙ g.
The graph of a function is given. Decide whether it iseven, odd, or neither.
38)
x-10 -8 -6 -4 -2 2 4 6 8 10
y108642
-2-4-6-8
-10
x-10 -8 -6 -4 -2 2 4 6 8 10
y108642
-2-4-6-8
-10
The graph of a function f is given. Use the graph toanswer the question.
39) For what numbers x is f(x) = 0?
100
-100 100
-100
MULTIPLE CHOICE. Choose the one alternative thatbest completes the statement or answers the question.
Match the graph to the function listed whose graph mostresembles the one given.
40)
A) reciprocal functionB) square root functionC) absolute value functionD) square function
5
SHORT ANSWER. Answer the question. SHOW ALLAPPROPRIATE WORK!
Solve the problem.41) To convert a temperature from degrees
Celsius to degrees Fahrenheit, you multiplythe temperature in degrees Celsius by 1.8 andthen add 32 to the result. Express F as a linearfunction of c.
Graph the function using its vertex, axis of symmetry,and intercepts.
42) f(x) = 4x2 - 32x + 65
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
Find the vertex and axis of symmetry of the graph of thefunction.
43) f(x) = -x2 + 4x
Solve the problem.44) A rock falls from a tower that is 160 ft high.
As it is falling, its height is given by theformula h = 160 - 16t2. How many secondswill it take for the rock to hit the ground (h =
0)?
45) The quadratic functionf(x) = 0.0037x2 - 0.43 x + 36.17 models themedian, or average, age, y, at which U.S. menwere first married x years after 1900. In whichyear was this average age at a minimum?(Round to the nearest year.) What was theaverage age at first marriage for that year?(Round to the nearest tenth.)
46) A developer wants to enclose a rectangulargrassy lot that borders a city street forparking. If the developer has 304 feet offencing and does not fence the side along thestreet, what is the largest area that can beenclosed?
Graph the function using its vertex, axis of symmetry,and intercepts.
47) f(x) = x2 + 12x
x-10 -5 5 10
y40
20
-20
-40
x-10 -5 5 10
y40
20
-20
-40
Determine the quadratic function whose graph is given.48)
x
y
(-2, -1)
(0, 3)
x
y
(-2, -1)
(0, 3)
6
Solve the problem.49) The following scatter diagram shows heights
(in inches) of children and their ages.
Height (inches)
x1 2 3 4 5 6 7 8 9 10 11 12 13 14
y66
60
54
48
42
36
30
24
18
12
6
x1 2 3 4 5 6 7 8 9 10 11 12 13 14
y66
60
54
48
42
36
30
24
18
12
6
Age (years)
What happens to height as age increases?
Graph the function. State whether it is increasing,decreasing, or constant..
50) f(x) = 5x + 3
x-8 -6 -4 -2 2 4 6 8
y8
6
4
2
-2
-4
-6
-8
x-8 -6 -4 -2 2 4 6 8
y8
6
4
2
-2
-4
-6
-8
Solve the problem.51) The cost in millions of dollars for a company
to manufacture x thousand automobiles isgiven by the function C(x) = 4x2 - 24x + 81.Find the number of automobiles that must beproduced to minimize the cost.
Graph the function f by starting with the graph of y = x2and using transformations (shifting, compressing,stretching, and/or reflection).
52) f(x) = -x2 + 6x - 3
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
Solve the inequality.53) 9x2 + 64 < 48x
Graph the function using its vertex, axis of symmetry,and intercepts.
54) f(x) = -x2 + 2x + 8
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
7
Plot a scatter diagram.55) Draw a scatter diagram of the given data.
Find the equation of the line containing thepoints (2.2, 8.1) and (4.6 , 3.0 ). Graph the lineon the scatter diagram.
x 1.4 2.2 2.8 3.6 4.6y 9.5 8.1 5.7 4.6 3.0
x1 2 3 4 5
y14
12
10
8
6
4
2
x1 2 3 4 5
y14
12
10
8
6
4
2
Use a graphing utility to find the equation of the line ofbest fit. Round to two decimal places, if necessary.
56) Managers rate employees according to jobperformance and attitude. The results forseveral randomly selected employees aregiven below.
PerformanceAttitude
59 63 65 69 58 77 76 69 70 6472 67 78 82 75 87 92 83 87 78
Solve the problem.57) A flare fired from the bottom of a gorge is
visible only when the flare is above the rim. Ifit is fired with an initial velocity of 176 ft/sec,and the gorge is 480 ft deep, during whatinterval can the flare be seen?(h = -16t2 + v0t + h0.)
Determine the average rate of change for the function.58) F(x) = -5
Graph the function f by starting with the graph of y = x2and using transformations (shifting, compressing,stretching, and/or reflection).
59) f(x) = x2 + 8x + 7
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
Determine the average rate of change for the function.60) p(x) = -x + 8
Use the graph to find the vertical asymptotes, if any, ofthe function.
61)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
List the potential rational zeros of the polynomialfunction. Do not find the zeros.
62) f(x) = 6x4 + 4x3 - 2x2 + 2
Use the Rational Zeros Theorem to find all the real zerosof the polynomial function. Use the zeros to factor f overthe real numbers.
63) f(x) = x4 - 12x2 - 64
8
Graph the function using transformations.
64) f(x) = 1x
- 3
x-5 5
y
5
-5
x-5 5
y
5
-5
State whether the function is a polynomial function ornot. If it is, give its degree. If it is not, tell why not.
65) f(x) = x( x -14)
Solve the problem.66) For what positive numbers will the cube of a
number exceed 9 times its square?
Find the indicated intercept(s) of the graph of thefunction.
67) y-intercept of f(x) = (x - 6)2
(x + 11)3
Use the Rational Zeros Theorem to find all the real zerosof the polynomial function. Use the zeros to factor f overthe real numbers.
68) f(x) = 3x4 - 6x3 + 4x2 - 2x + 1
Find the indicated intercept(s) of the graph of thefunction.
69) y-intercept of f(x) = x - 7x2 + 11x - 12
Give the equation of the horizontal asymptote, if any, ofthe function.
70) g(x) = x2 + 8x - 5x - 5
Solve the inequality algebraically. Express the solutionin interval notation.
71) x2(x - 11)(x + 1)(x - 4)(x + 8)
≥ 0
For the polynomial, list each real zero and itsmultiplicity. Determine whether the graph crosses ortouches the x-axis at each x -intercept.
72) f(x) = 13x2(x2 - 5 )
Use the Rational Zeros Theorem to find all the real zerosof the polynomial function. Use the zeros to factor f overthe real numbers.
73) f(x) = 3x3 - 2x2 + 6x - 4
Find the x- and y-intercepts of f.74) f(x) = (x + 6)(x - 4)(x + 4)
Give the equation of the oblique asymptote, if any, ofthe function.
75) h(x) = 3x2 - 7x - 2
6x2 - 9x + 9
Use the graph to find the vertical asymptotes, if any, ofthe function.
76)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
Find the intercepts of the function f(x).77) f(x) = 4x - x3
Find the indicated intercept(s) of the graph of thefunction.
78) y-intercept of f(x) = 5xx2 - 19
9
State whether the function is a polynomial function ornot. If it is, give its degree. If it is not, tell why not.
79) f(x) = 1 + 9x
Use the graph of the function f to solve the inequality.80) f(x) < 0
x-10 -8 -6 -4 -2 2 4 6 8 10
y
x-10 -8 -6 -4 -2 2 4 6 8 10
y
Find the domain of the composite function f ∘ g.
81) f(x) = 2x + 1
; g(x) = x + 10
Solve the problem.82) During its first year of operation, 200,000
people visited Rave Amusement Park. Sixyears later, the number had grown to 834,000.If the number of visitors to the park obeys thelaw of uninhibited growth, find theexponential growth function that models thisdata.
83) Between 7:00 AM and 8:00 AM, trains arriveat a subway station at a rate of 10 trains perhour (0.17 trains per minute). The followingformula from statistics can be used todetermine the probability that a train willarrive within t minutes of 7:00 AM.
F(t) = 1 - e-0.17tDetermine how many minutes are needed forthe probability to reach 40%.
Solve the equation.84) log3 (x + 2) = 2 + log3 (x - 3 )
85) 17x
= 49
Solve the problem.86) f(x) = log3(x + 1) and g(x) = log3(x - 4).
Solve g(x) = 129. What point is on the graphof g?
Solve the equation.
87) 32x
= 827
88) log3 x + log3(x - 24) = 4
Write as the sum and/or difference of logarithms. Expresspowers as factors.
89) log 1 - 1x3
Solve the problem.90) The long jump record, in feet, at a particular
school can be modeled byf(x) = 18.2 + 2.4 ln(x + 1) where x is the numberof years since records began to be kept at theschool. What is the record for the long jump15 years after record started being kept?Round your answer to the nearest tenth.
For the given functions f and g, find the requestedcomposite function value.
91) f(x) = 7x + 8, g(x) = -1/x; Find (g ∘ f)(3).
Use transformations to graph the function. Determinethe domain, range, and horizontal asymptote of thefunction.
92) f(x) = 5-x + 2
x-4 -2 2 4 6
y
4
2
-2
-4
x-4 -2 2 4 6
y
4
2
-2
-4
10
Solve the problem.93) The formula P = 14.7e-0.21x gives the
average atmospheric pressure, P, in poundsper square inch, at an altitude x, in milesabove sea level. Find the average atmosphericpressure for an altitude of 2.3 miles. Roundyour answer to the nearest tenth.
Express as a single logarithm.94) 7ln (x - 8) - 2 ln x
MULTIPLE CHOICE. Choose the one alternative thatbest completes the statement or answers the question.
The graph of a logarithmic function is shown. Select thefunction which matches the graph.
95)
x-5 5
y
5
-5
x-5 5
y
5
-5
A) y = log x - 2 B) y = 2 - log xC) y = log(2 - x) D) y = log(x - 2)
SHORT ANSWER. Answer the question. SHOW ALLAPPROPRIATE WORK!
Express as a single logarithm.96) log x + log (x2 - 169) - log 9 - log (x - 13)
Solve the equation.97) log11 x2 = 4
Solve the problem.98) Gillian has $10,000 to invest in a mutual fund.
The average annual rate of return for the pastfive years was 12.25%. Assuming this rate,determine how long it will take for herinvestment to double.
Decide whether the composite functions, f ∘ g and g ∘ f,are equal to x.
99) f(x) = x , g(x) = x2
Solve the problem.100) A fully cooked turkey is taken out of an oven
set at 200 °C (Celsius) and placed in a sink ofchilled water of temperature 4°C. After 3minutes, the temperature of the turkey ismeasured to be 50°C. How long (to thenearest minute) will it take for thetemperature of the turkey to reach 15°C?Assume the cooling follows Newton's Law ofCooling:
U = T + (Uo - T)ekt.(Round your answer to the nearest minute.)
Find the period.101) y = -5 cos(5πx + 4)
Solve the problem.102) Before exercising, an athlete measures her air
flow and obtains
a = 0.65 sin 2π5t
where a is measured in liters per second and tis the time in seconds. If a > 0, the athlete isinhaling; if a < 0, the athlete is exhaling. Thetime to complete one completeinhalation/exhalation sequence is arespiratory cycle. What is the amplitude? What is the period?What is the respiratory cycle? Graph a over two periods beginning at t = 0.
t5 10
a1
-1
t5 10
a1
-1
11
Convert the angle in degrees to radians. Express theanswer as multiple of π.
103) 87°
Find an equation for the graph.104)
Solve the problem.105) For what numbers θ is f(θ) = csc θ not
defined?
Find the phase shift.
106) y = -3 sin 14x - π
4
If A denotes the area of the sector of a circle of radius rformed by the central angle θ, find the missing quantity.If necessary, round the answer to two decimal places.
107) r = 88.4 centimeters, θ = π5
radians, A = ?
Use the even-odd properties to find the exact value ofthe expression. Do not use a calculator.
108) sec - π6
Convert the angle in radians to degrees.
109) - 7π6
Solve the problem.110) A rotating beacon is located 4 ft from a wall.
If the distance from the beacon to the point onthe wall where the beacon is aimed is givenby a = 4|sec (2πt)| , where t is in seconds,find a when t = 0.40 seconds. Round youranswer to the nearest hundredth.
Find the exact value. Do not use a calculator.111) cot 45 °
Use the properties of the trigonometric functions to findthe exact value of the expression. Do not use a calculator.
112) sin2 55° + cos2 55°
Find the amplitude.
113) y = -3 cos 4x + π2
In the problem, sin θ and cos θ are given. Find the exactvalue of the indicated trigonometric function.
114) sin θ = 53, cos θ =
23
Find tan θ.
Find (i) the amplitude, (ii) the period, and (iii) the phaseshift.
115) y = - 12
sin(4x + 3π)
Write the equation of a sine function that has the givencharacteristics.
116) Amplitude: 4Period: 3π
Phase Shift: - π3
Find the area A. Round the answer to three decimalplaces.
117)
π5
10 m
Find the exact value of the expression if θ = 45°. Do notuse a calculator.
118) f(θ) = cos θ Find 11f(θ).
Use the even-odd properties to find the exact value ofthe expression. Do not use a calculator.
119) sec (-60°)
12
Find the exact value of the expression. Do not use acalculator.
120) sin π3
- cos π6
Use a calculator to find the value of the expressionrounded to two decimal places.
121) sin-1 35
Find the exact solution of the equation.
122) -sin-1(4x) = π4
Find the exact value, if any, of the composite function. Ifthere is no value, say it is "not defined". Do not use acalculator.
123) sin(sin-1 1.8)
Find the exact solution of the equation.124) 3 sin-1 x = π
125) -3 sin-1(2x) = π
Find the exact value of the expression.
126) cos sin-1 45
127) sin cos-1 - 35
128) tan(cos-1 1)
129) sec-1 -1
130) sin cos-1 - 22
Solve the equation on the interval 0 ≤ θ < 2π.131) 2 cos2 θ - 1 = 0
Solve the equation. Give a general formula for all thesolutions.
132) cos(2θ) = 22
Solve the equation on the interval 0 ≤ θ < 2π.
133) cot 2θ - π2
= 1
134) 1 + cos θ = 2 sin2 θ
Use a calculator to solve the equation on the interval 0 ≤θ < 2π. Round the answer to two decimal places.
135) csc θ = -5
Establish the identity.
136) 1 - cot2v1 + cot2v
+ 1 = 2 sin2v
137) (tan v + 1)2 + (tan v - 1)2 = 2 sec2v
138) 1 + csc xsec x
= cos x + cot x
139) 5 csc2 x + 4 csc x - 1
cot 2 x = 5 csc x - 1csc x - 1
140) 1 - sin tcos t
= cos t1 + sin t
13
Answer KeyTestname: FALL FINAL REVIEW 2017
1) (0, -14), (18.67, 0)ID: PCEGU6 1.1.7-5Objective: (1.1) Use a Graphing Utility to Approximate
Intercepts2) (-1.5 , -1)ID: PCEGU6 1.1.2-4Objective: (1.1) Use the Midpoint Formula
3) (h, k) = (-9, -2); r = 6ID: PCEGU6 1.5.3-4Objective: (1.5) Work with the General Form of the
Equation of a Circle4) NoID: PCEGU6 1.1.1-15Objective: (1.1) Use the Distance Formula
5) {5, 6}ID: PCEGU6 1.3.1-14Objective: (1.3) Solve Equations Using a Graphing Utility
6)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
ID: PCEGU6 1.5.2-7Objective: (1.5) Graph a Circle
7) y = -44x + 134ID: PCEGU6 1.4.5-15Objective: (1.4) Find the Equation of a Line Given Two
Points8) (0, -3), (-9, 0), (0, 3)ID: PCEGU6 1.2.1-3Objective: (1.2) Find Intercepts from an Equation
9) undefinedID: PCEGU6 1.4.1-9Objective: (1.4) Calculate and Interpret the Slope of a Line
10)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
ID: PCEGU6 1.2.3-2Objective: (1.2) Know How to Graph Key Equations
11) 2 5ID: PCEGU6 1.1.1-10Objective: (1.1) Use the Distance Formula
12) (0, -6.8), (-3.37, 0), (3.37, 0)ID: PCEGU6 1.1.7-7Objective: (1.1) Use a Graphing Utility to Approximate
Intercepts13) (h, k) = (-3, -6); r = 3
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
ID: PCEGU6 1.5.3-2Objective: (1.5) Work with the General Form of the
Equation of a Circle
14) x2 + (y + 2)2 = 2ID: PCEGU6 1.5.1-8Objective: (1.5) Write the Standard Form of the Equation
of a Circle15) y = - 3400x + 17,000 ;
value after 2 years is $10,200 .00;ID: PCEGU6 1.4.5-10Objective: (1.4) Find the Equation of a Line Given Two
Points
14
Answer KeyTestname: FALL FINAL REVIEW 2017
16) slope = 47; y-intercept = - 1
7ID: PCEGU6 1.4.7-6Objective: (1.4) Identify the Slope and y-Intercept of a
Line from Its Equation
17) slope = - 35
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
ID: PCEGU6 1.4.8-5Objective: (1.4) Graph Lines Written in General Form
Using Intercepts18) y = 0.25 x + 0.45
ID: PCEGU6 1.4.5-14Objective: (1.4) Find the Equation of a Line Given Two
Points19)
x-5 5
y
5
-5
x-5 5
y
5
-5
y-axisID: PCEGU6 1.1.3-5Objective: (1.1) Graph Equations by Hand by Plotting
Points20) no solution
ID: PCEGU6 1.3.1-2Objective: (1.3) Solve Equations Using a Graphing Utility
21) y = x2 - 7ID: PCEGU6 2.5.1-3Objective: (2.5) Graph Functions Using Vertical and
Horizontal Shifts
22) local maximum at (0, 1)local minimum at (2, -3)ID: PCEGU6 2.3.6-8Objective: (2.3) Use Graphing Utility to Approximate
Local Maxima/Minima & Determine WhereFunc is Increasing/Decreasing
23)
x-5 5
y
5
-5
x-5 5
y
5
-5
ID: PCEGU6 2.5.2-8Objective: (2.5) Graph Functions Using Compressions and
Stretches24) negative
ID: PCEGU6 2.2.2-3Objective: (2.2) Obtain Information from or about the
Graph of a Function25) 14
ID: PCEGU6 2.3.7-6Objective: (2.3) Find the Average Rate of Change of a
Function26) even
ID: PCEGU6 2.3.2-8Objective: (2.3) Identify Even and Odd Functions from
the Equation27) none
ID: PCEGU6 2.2.2-23Objective: (2.2) Obtain Information from or about the
Graph of a Function28) even
ID: PCEGU6 2.3.1-1Objective: (2.3) Determine Even and Odd Functions from
a Graph29) About 6 fish
ID: PCEGU6 2.1.2-20Objective: (2.1) Find the Value of a Function
30) (0, 4)ID: PCEGU6 2.4.2-10Objective: (2.4) Graph Piecewise-defined Functions
15
Answer KeyTestname: FALL FINAL REVIEW 2017
31) Absolute maximum: none; Absolute minimum: f(1)= 2ID: PCEGU6 2.3.5-3Objective: (2.3) Use a Graph to Locate the Absolute
Maximum and the Absolute Minimum32) A
ID: PCEGU6 2.2.2-26Objective: (2.2) Obtain Information from or about the
Graph of a Function33) even
ID: PCEGU6 2.3.1-2Objective: (2.3) Determine Even and Odd Functions from
a Graph
34) - 23
ID: PCEGU6 2.1.2-2Objective: (2.1) Find the Value of a Function
35) AID: PCEGU6 2.5.1-2Objective: (2.5) Graph Functions Using Vertical and
Horizontal Shifts36) odd
ID: PCEGU6 2.3.1-7Objective: (2.3) Determine Even and Odd Functions from
a Graph
37) (f ∙ g)(x) = (5 - x)(x - 1); {x|1 ≤ x ≤ 5}ID: PCEGU6 2.1.4-9Objective: (2.1) Form the Sum, Difference, Product, and
Quotient of Two Functions38) odd
ID: PCEGU6 2.3.1-6Objective: (2.3) Determine Even and Odd Functions from
a Graph39) -60, 70, 100
ID: PCEGU6 2.2.2-4Objective: (2.2) Obtain Information from or about the
Graph of a Function40) A
ID: PCEGU6 2.4.1-7Objective: (2.4) Graph the Functions Listed in the Library
of Functions41) F(c) = 1.8c + 32
ID: PCEGU6 3.1.4-8Objective: (3.1) Build Linear Models from Verbal
Descriptions
42) vertex (4, 1)intercept (0, 65)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
ID: PCEGU6 3.3.3-8Objective: (3.3) Graph a Quadratic Function Using Its
Vertex, Axis, and Intercepts43) (2, 4); x = 2
ID: PCEGU6 3.3.2-3Objective: (3.3) Identify the Vertex and Axis of Symmetry
of a Quadratic Function44) 3.2 s
ID: PCEGU6 3.5.1-25Objective: (3.5) Solve Inequalities Involving a Quadratic
Function45) 1958, 23.7 years old
ID: PCEGU6 3.4.1-8Objective: (3.4) Build Quadratic Models from Verbal
Descriptions
46) 11,552 ft2ID: PCEGU6 3.3.5-18Objective: (3.3) Find the Maximum or Minimum Value of
a Quadratic Function47) vertex (-6, -36)
intercepts (0, 0), (- 12, 0)
x-10 -5 5 10
y40
20
-20
-40
x-10 -5 5 10
y40
20
-20
-40
ID: PCEGU6 3.3.3-1Objective: (3.3) Graph a Quadratic Function Using Its
Vertex, Axis, and Intercepts
16
Answer KeyTestname: FALL FINAL REVIEW 2017
48) f(x) = x2 + 4x + 3ID: PCEGU6 3.3.4-2Objective: (3.3) Find a Quadratic Function Given Its
Vertex and One Other Point49) Height increases as age increases.
ID: PCEGU6 3.2.1-8Objective: (3.2) Draw and Interpret Scatter Diagrams
50) increasing
x-8 -6 -4 -2 2 4 6 8
y8
6
4
2
-2
-4
-6
-8
x-8 -6 -4 -2 2 4 6 8
y8
6
4
2
-2
-4
-6
-8
ID: PCEGU6 3.1.3-1Objective: (3.1) Determine Whether a Linear Function Is
Increasing, Decreasing, or Constant51) 3 thousand automobiles
ID: PCEGU6 3.4.1-12Objective: (3.4) Build Quadratic Models from Verbal
Descriptions52)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
ID: PCEGU6 3.3.1-15Objective: (3.3) Graph a Quadratic Function Using
Transformations
53) -∞, 83
ID: PCEGU6 3.5.1-17Objective: (3.5) Solve Inequalities Involving a Quadratic
Function
54) vertex (1, 9)intercepts (4, 0), (- 2, 0), (0, 8)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
ID: PCEGU6 3.3.3-7Objective: (3.3) Graph a Quadratic Function Using Its
Vertex, Axis, and Intercepts55) y = -2.12x + 12.78
x1 2 3 4 5
y14
12
10
8
6
4
2
x1 2 3 4 5
y14
12
10
8
6
4
2
ID: PCEGU6 3.2.1-4Objective: (3.2) Draw and Interpret Scatter Diagrams
56) y = 1.02x + 11.7ID: PCEGU6 3.2.3-15Objective: (3.2) Use a Graphing Utility to Find the Line of
Best Fit57) 5 < t < 6
ID: PCEGU6 3.5.1-27Objective: (3.5) Solve Inequalities Involving a Quadratic
Function58) 0
ID: PCEGU6 3.1.2-4Objective: (3.1) Use Average Rate of Change to Identify
Linear Functions
17
Answer KeyTestname: FALL FINAL REVIEW 2017
59)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
ID: PCEGU6 3.3.1-12Objective: (3.3) Graph a Quadratic Function Using
Transformations60) -1
ID: PCEGU6 3.1.2-3Objective: (3.1) Use Average Rate of Change to Identify
Linear Functions61) x = 3
ID: PCEGU6 4.4.2-14Objective: (4.4) Find the Vertical Asymptotes of a Rational
Function
62) ± 16, ± 13, ± 12, ± 23, ± 1, ± 2
ID: PCEGU6 4.2.2-2Objective: (4.2) Use the Rational Zeros Theorem to List
the Potential Rational Zeros of a PolynomialFunction
63) -4, 4; f(x) = (x - 4)(x + 4)(x2 + 4)ID: PCEGU6 4.2.3-1Objective: (4.2) Find the Real Zeros of a Polynomial
Function64)
x-5 5
y
5
-5
x-5 5
y
5
-5
ID: PCEGU6 4.4.4-2Objective: (4.4) Demonstrate Additional Understanding
and Skills
65) No; x is raised to non-integer powerID: PCEGU6 4.1.1-12Objective: (4.1) Identify Polynomial Functions and Their
Degree66) {x|x > 9}; (9 , ∞)
ID: PCEGU6 4.6.1-20Objective: (4.6) Solve Polynomial Inequalities
Algebraically and Graphically
67) 0, 361331
ID: PCEGU6 4.5.1-14Objective: (4.5) Analyze the Graph of a Rational Function
68) 1, 1; f(x) = (x - 1)2(3x2 + 1)ID: PCEGU6 4.2.3-6Objective: (4.2) Find the Real Zeros of a Polynomial
Function
69) 0, 712
ID: PCEGU6 4.5.1-12Objective: (4.5) Analyze the Graph of a Rational Function
70) no horizontal asymptotesID: PCEGU6 4.4.3-2Objective: (4.4) Find the Horizontal or Oblique
Asymptotes of a Rational Function71) (-∞, -8) ∪ [-1, 4) ∪ [11, ∞)
ID: PCEGU6 4.6.2-16Objective: (4.6) Solve Rational Inequalities Algebraically
and Graphically72) 0, multiplicity 2, touches x-axis;
5 , multiplicity 1, crosses x-axis;- 5, multiplicity 1, crosses x-axisID: PCEGU6 4.1.3-14Objective: (4.1) Identify the Real Zeros of a Polynomial
Function and Their Multiplicity
73) 23; f(x) = (3x - 2)(x2 + 2)
ID: PCEGU6 4.2.3-4Objective: (4.2) Find the Real Zeros of a Polynomial
Function74) x-intercepts: -6, -4, 4; y-intercept: -96
ID: PCEGU6 4.1.4-3Objective: (4.1) Analyze the Graph of a Polynomial
Function75) no oblique asymptote
ID: PCEGU6 4.4.3-17Objective: (4.4) Find the Horizontal or Oblique
Asymptotes of a Rational Function
18
Answer KeyTestname: FALL FINAL REVIEW 2017
76) x = 0ID: PCEGU6 4.4.2-16Objective: (4.4) Find the Vertical Asymptotes of a Rational
Function77) x-intercepts: 0, 2, -2; y-intercept: 0
ID: PCEGU6 4.2.3-17Objective: (4.2) Find the Real Zeros of a Polynomial
Function78) (0, 0)
ID: PCEGU6 4.5.1-11Objective: (4.5) Analyze the Graph of a Rational Function
79) No; x is raised to a negative powerID: PCEGU6 4.1.1-6Objective: (4.1) Identify Polynomial Functions and Their
Degree80) (-3, 2) ∪ (4, ∞)
ID: PCEGU6 4.6.1-3Objective: (4.6) Solve Polynomial Inequalities
Algebraically and Graphically81) {x x ≠ -11}
ID: PCEGU6 5.1.2-2Objective: (5.1) Find the Domain of a Composite Function
82) f(t) = 200,000e0.238tID: PCEGU6 5.8.1-3Objective: (5.8) Find Equations of Populations That Obey
the Law of Uninhibited Growth83) 3.00 min
ID: PCEGU6 5.4.5-23Objective: (5.4) Solve Logarithmic Equations
84) 298
ID: PCEGU6 5.6.1-11Objective: (5.6) Solve Logarithmic Equations
85) {-2}ID: PCEGU6 5.3.4-8Objective: (5.3) Solve Exponential Equations
86) {5}, (5 , 129)ID: PCEGU6 5.6.1-16Objective: (5.6) Solve Logarithmic Equations
87) {-3}ID: PCEGU6 5.3.4-9Objective: (5.3) Solve Exponential Equations
88) {27}ID: PCEGU6 5.6.1-7Objective: (5.6) Solve Logarithmic Equations
89) log(x - 1) + log(x2 + x + 1) - 3 log xID: PCEGU6 5.5.2-13Objective: (5.5) Write a Logarithmic Expression as a Sum
or Difference of Logarithms
90) 24.9 ftID: PCEGU6 5.4.2-17Objective: (5.4) Evaluate Logarithmic Expressions
91) - 129
ID: PCEGU6 5.1.1-8Objective: (5.1) Form a Composite Function
92)
x-4 -2 2 4 6
y6
4
2
-2
-4
-6
x-4 -2 2 4 6
y6
4
2
-2
-4
-6
domain of f: (-∞, ∞); range of f:(2, ∞) horizontal asymptote: y = 2ID: PCEGU6 5.3.2-8Objective: (5.3) Graph Exponential Functions
93) 9.1 lb/in.2ID: PCEGU6 5.3.3-15Objective: (5.3) Define the Number e
94) ln (x - 8)7
x2
ID: PCEGU6 5.5.3-5Objective: (5.5) Write a Logarithmic Expression as a
Single Logarithm95) A
ID: PCEGU6 5.4.4-1Objective: (5.4) Graph Logarithmic Functions
96) log x(x + 13)9
ID: PCEGU6 5.5.3-10Objective: (5.5) Write a Logarithmic Expression as a
Single Logarithm97) {121, -121}
ID: PCEGU6 5.4.5-3Objective: (5.4) Solve Logarithmic Equations
98) 6 yrID: PCEGU6 5.7.4-7Objective: (5.7) Determine the Rate of Interest or Time
Required to Double a Lump Sum of Money
19
Answer KeyTestname: FALL FINAL REVIEW 2017
99) Yes, yesID: PCEGU6 5.1.1-24Objective: (5.1) Form a Composite Function
100) 6 minutesID: PCEGU6 5.8.3-8Objective: (5.8) Use Newton's Law of Cooling
101) 25ID: PCEGU6 6.6.1-14Objective: (6.6) Graph Sinusoidal Functions of the Form y
= A sin (ωx - φ) + B102) amplitude = 0.65, period = 5, respiratory cycle = 5
seconds
a = 0.65sin 2π5t
t5 10
a
0.65
-0.65
t5 10
a
0.65
-0.65
ID: PCEGU6 6.4.3-16Objective: (6.4) Determine the Amplitude and Period of
Sinusoidal Functions
103) 29π60ID: PCEGU6 6.1.3-5Objective: (6.1) Convert from Degrees to Radians and
from Radians to Degrees
104) y = -3 cos 13x
ID: PCEGU6 6.4.5-13Objective: (6.4) Find an Equation for a Sinusoidal Graph
105) integral multiples of π (180°)ID: PCEGU6 6.3.1-3Objective: (6.3) Determine the Domain and the Range of
the Trigonometric Functions
106) π units to the rightID: PCEGU6 6.6.1-19Objective: (6.6) Graph Sinusoidal Functions of the Form y
= A sin (ωx - φ) + B
107) 2455 cm2ID: PCEGU6 6.1.4-7Objective: (6.1) Find the Area of a Sector of a Circle
108) 2 33
ID: PCEGU6 6.3.6-7Objective: (6.3) Use Even-Odd Properties to Find the
Exact Values of the Trigonometric Functions109) -210°
ID: PCEGU6 6.1.3-8Objective: (6.1) Convert from Degrees to Radians and
from Radians to Degrees110) 4.94 ft
ID: PCEGU6 6.5.2-9Objective: (6.5) Graph Functions of the Form y = A csc
(ωx) + B and y = A sec (ωx) + B111) 1
ID: PCEGU6 6.2.3-2Objective: (6.2) Find the Exact Values of the Trigonometric
Functions of pi/4 = 45°112) 1
ID: PCEGU6 6.3.4-5Objective: (6.3) Find the Values of the Trigonometric
Functions Using Fundamental Identities113) 3
ID: PCEGU6 6.6.1-3Objective: (6.6) Graph Sinusoidal Functions of the Form y
= A sin (ωx - φ) + B
114) 52
ID: PCEGU6 6.3.4-1Objective: (6.3) Find the Values of the Trigonometric
Functions Using Fundamental Identities
115) (i) 12
(ii) π2
(iii) - 3π4
ID: PCEGU6 6.6.1-1Objective: (6.6) Graph Sinusoidal Functions of the Form y
= A sin (ωx - φ) + B
116) y = 4 sin 23x + 29π
ID: PCEGU6 6.6.1-24Objective: (6.6) Graph Sinusoidal Functions of the Form y
= A sin (ωx - φ) + B
20
Answer KeyTestname: FALL FINAL REVIEW 2017
117) 31.416 m2ID: PCEGU6 6.1.4-10Objective: (6.1) Find the Area of a Sector of a Circle
118) 11 22
ID: PCEGU6 6.2.3-5Objective: (6.2) Find the Exact Values of the Trigonometric
Functions of pi/4 = 45°119) 2
ID: PCEGU6 6.3.6-3Objective: (6.3) Use Even-Odd Properties to Find the
Exact Values of the Trigonometric Functions120) 0
ID: PCEGU6 6.2.4-8Objective: (6.2) Find the Exact Values of the Trigonometric
Functions of pi/6 = 30° and pi/3 = 60°121) 0.64
ID: PCEGU6 7.1.2-4Objective: (7.1) Find an Approximate Value of the Inverse
Sine, Cosine, and Tangent Functions
122) x = - 28
ID: PCEGU6 7.1.5-8Objective: (7.1) Solve Equations Involving Inverse
Trigonometric Functions123) not defined
ID: PCEGU6 7.1.3-16Objective: (7.1) Use Properties of Inverse Functions to
Find Exact Values of Certain CompositeFunctions
124) x = 32
ID: PCEGU6 7.1.5-4Objective: (7.1) Solve Equations Involving Inverse
Trigonometric Functions
125) x = - 34
ID: PCEGU6 7.1.5-12Objective: (7.1) Solve Equations Involving Inverse
Trigonometric Functions
126) 35ID: PCEGU6 7.2.1-22Objective: (7.2) Find the Exact Value of Expressions
Involving the Inverse Sine, Cosine, andTangent Functions
127) 45ID: PCEGU6 7.2.1-25Objective: (7.2) Find the Exact Value of Expressions
Involving the Inverse Sine, Cosine, andTangent Functions
128) 0ID: PCEGU6 7.2.1-7Objective: (7.2) Find the Exact Value of Expressions
Involving the Inverse Sine, Cosine, andTangent Functions
129) πID: PCEGU6 7.2.2-3Objective: (7.2) Define the Inverse Secant, Cosecant, and
Cotangent Functions
130) 22
ID: PCEGU6 7.2.1-4Objective: (7.2) Find the Exact Value of Expressions
Involving the Inverse Sine, Cosine, andTangent Functions
131) π4, 3π4, 5π4, 7π4
ID: PCEGU6 7.3.1-7Objective: (7.3) Solve Equations Involving a Single
Trigonometric Function
132) θ|θ = π8
+ kπ, θ = 7π8
+ kπ
ID: PCEGU6 7.3.1-34Objective: (7.3) Solve Equations Involving a Single
Trigonometric Function
133) 3π8, 7π8, 11π8, and 15π
8ID: PCEGU6 7.3.1-25Objective: (7.3) Solve Equations Involving a Single
Trigonometric Function
134) π3, π, 5π
3ID: PCEGU6 7.3.4-10Objective: (7.3) Solve Trigonometric Equations Using
Fundamental Identities135) 6.08 , 3.34
ID: PCEGU6 7.3.2-7Objective: (7.3) Solve Trigonometric Equations Using a
Calculator
21
Answer KeyTestname: FALL FINAL REVIEW 2017
136) 1 - cot2v1 + cot2v
+ 1 = 1 - cot2v csc2v
+ 1 = 1 csc2v
- cot2v
csc2v + 1
= sin2v -
cos2vsin2v
1sin2v
+ 1
= sin2v - cos2v + (sin2v + cos2v) = 2 sin2vID: PCEGU6 7.4.2-25Objective: (7.4) Establish Identities
137) (tan v + 1)2 + (tan v - 1)2 = tan2v + 2 tan v + 1 + tan2v- 2 tan v + 1 = 2(tan2v + 1) = 2 sec2vID: PCEGU6 7.4.2-11Objective: (7.4) Establish Identities
138) 1 + csc xsec x
= cos x 1 + 1sin x
= cos x (sin x + 1)sinx
=
cos x sin xsin x
+ cos xsin x
= cos x + cot x.
ID: PCEGU6 7.4.2-37Objective: (7.4) Establish Identities
139) 5 csc2 x + 4 csc x - 1
cot2 x = (5 csc x - 1) (csc x + 1)
csc2 x - 1 =
(5 csc x - 1) (csc x + 1)(csc x - 1) (csc x + 1)
= 5 csc x - 1csc x - 1
.
ID: PCEGU6 7.4.2-56Objective: (7.4) Establish Identities
140) 1 - sin tcos t
= 1 + sin t1 + sin t
1 - sin tcos t
= cos 2 tcos t (1 + sin t)
=
cos t1 + sin t
.
ID: PCEGU6 7.4.2-45Objective: (7.4) Establish Identities
22