math 1314 - college algebra review for test 1 · math 1314 - college algebra review for test 1...

MATH 1314 - College Algebra Review for Test 1

Section 1.1 1. Classify each of the following as one or more of the following: natural number, integer, rational number, or irrational number.

(a) –5 (b)

€

7 (c)

€

23

(d) 3.97 (e)

€

0.257

2. Evaluate each of the following: (a)

€

−42 − 2 3 + 5( )2 (b)

€

−24 ÷ 3 × 2 +−3 +17−9 + 2

3. Write each of the following in scientific notation: (a) 0.000395 (b) 54,300 4. Write each of the following in standard notation: (a)

€

5.38 ×10−4 (b)

€

9.24 ×104

5. Multiply and give your answer in scientific notation:

€

6 ×10−5( ) 7 ×102( )

6. Rachel’s weekly pay increased from $125 to $140. What was the percent change in her weekly pay? Section 1.2 7. What is the mean of the set of numbers {72, 88, 96, 84}? 8. What is the median of the set of numbers {72, 88, 96, 84}? 9. Find the exact distance between the points (4,–5) and (–2,–1). 10. Find the midpoint of the line segment connecting the points (4,–5) and (–2,–1). 11. For the relation {(

€

−3 ,4), (1,2), (5,

€

−6)}, (a) what is the domain and (b) what is the range? 12. Give the standard form of the equation of the circle shown at the right.

1 x

y

1

MATH 1314 - College Algebra - Review for Test 1 (Thomason) - p. 2 of 8

13. Give (a) the center and (b) the radius of the circle whose equation is

€

(x − 7)2 + ( y + 5)2 = 4. 14. Give the standard form of the equation of the circle that has its center at (4,–3) with the point (–1,9) on the circle. 15. Give the standard form of the equation of the circle that has ends of a diameter at (–3,4) and (7,–6). Section 1.3 16. (a) Is the set of ordered pairs {(1,3),(4,4), (3,1)} a function? Explain how you know. (b) Is the relation whose graph is shown at the right a function? Explain how you know.

(c) Is the relation given by the following table a function? Explain how you know.

X 1 3 4 3 Y –5 3 0 2

17. Determine the domain of each of the following functions.

(a)

€

f (x) =2

x2 − 25 (b)

€

g(x) = x2 + 2 (c)

€

h( x) = 3x − 2

18. For

€

f ( x) = −x2 + 5, determine (a)

€

f (−3) , (b)

€

f (4), and (c)

€

f (a + 2) . 19. (a) True or False: The graph of

€

4y +12 = 0 is a vertical line that passes through –3 on the x-axis. (b) True or False: The slope of the line

€

3x +12 = 0 is undefined. 20. The graph of f is shown at the right. (a) What is the range of f? (b) Determine

€

f (−2). (c) Determine the value(s) of x for which

€

f (x) = 2

x

y

1

1

x

y

1

1


Section 1.4 21. The graph shown at the right shows the price of x yards of carpeting. (a) Find the slope of the graph. (b) Interpret the slope as a rate of change.

Section 1.5 22. Express the following in interval notation:

€

{x −3 ≤ x < 5} 23. Express the following in interval notation:

24. Use the graph of f at the right to determine the interval(s) in which (a) f is increasing and (b) f is decreasing. Give your answers in interval notation.

25. For

€

f ( x) = −x2 − 2x + 3, compute the average rate of change of f from

€

x1 = −2 to

€

x2 =1. 26. For

€

f (x) = 3x2 − 5x + 4 , (a) determine

€

f (x + h) and (b) determine the difference quotient

€

f (x + h) − f (x)h

and simplify.

Section 2.1 27. (a) Is the data in the table at the right linear? (b) If so, determine the slope-intercept form of the equation of the line passing through the data points?

x 0 3 6 9 y 2 6 10 14

1 x

y

2 3 4 5 6 7 8 9 10

1428425670

Carpet (square yards)

0 1 2 3 4 5–1–2–3–4–5(]

1 x

y

1


28. Write a formula for the linear function f show in the graph at the right.

29. For

€

f (x) = −32x + 6 , (a) give the slope, (b) give the x-intercept, (c) give the y-

intercept, and (d) draw the graph. 30. For

€

−4x + 5y = 20 , (a) give the slope, (b) give the x-intercept, (c) give the y-intercept, and (d) draw the graph. 31. For

€

3y = −12, (a) give the slope, (b) give the x-intercept, (c) give the y-intercept, and (d) draw the graph. 32. For

€

2x −10 = 0, (a) give the slope, (b) give the x-intercept, (c) give the y-intercept, and (d) draw the graph.

33. For the piecewise function f is defined by

€

f (x) =4 if x ≤ 2−x + 3 if x > 2⎧ ⎨ ⎩

, determine

(a)

€

f (−3) and (b)

€

f (3) . (c) Graph f . Section 2.2 34. A person is riding a bicycle along a straight highway. The graph at the right shows the rider’s distance y in miles from a First Aid Station after x hours. (a) Find the slope-intercept form of the equation of the line. (b) How fast is the bicyclist traveling? (c) How far from the First Aid Station was the bicyclist initially? (d) How far from the First Aid Station was the bicyclist after 2 hours? 35. Determine the slope-intercept form of the equation of the line that is perpendicular to

€

y =23x −12 and that passes through the point (6,–1)

1 x

y

1

x

y

0 1 2 3 4 5 6

5101520253035

(1,13)

(4,31)


36. Determine the slope-intercept form of the equation of the line that is parallel to

€

3x + 4y =12 and that passes through the point (12,–5). 37. In 2005, the number of homes in the U.S. with flat screen televisions was 17.5 million. Since then, the number of homes in the U.S. with flat screen televisions has been increasing at a constant rate of 8.2 million homes per year. Let t represent the number of years since 2005 and write a formula for the linear function N that models this situation. 38. In 2000 there were 7.6 million automobiles produced in the United States and in 2004 there were 6.4 million. The formula

€

V (t) = −0.3t + 7.6 models these data exactly, where

€

t = 0 corresponds to 2000,

€

t =1 to 2001, and so on. Use

€

V (t) to estimate the number of automobiles manufactured in the U. S. in 2009. 39. In 1998 the value of a house was $150,000 and in 2006 the value of the house was $182,000. Find a linear function V that approximates the value of the house in year x. 40. Suppose y is direction proportional to x and that

€

y =12 when

€

x = 7. Find y if

€

x =10. 41. The cost of tuition is directly proportional to the number of credit hours taken. If 12 credit hours cost $528, what would be the cost of 15 credit hours. Section 2.3 42. Solve the equation:

€

−2(3x − 4) − 5 = 6 − (x −1)

43. Solve the equation:

€

23x − 3

4=56x +

712

44. Solve for b:

€

3a − 5b = 8 45. Jelly Beans sell for $2 a pound and Gummy Bears sell for $3 a pound. How many pounds of each kind of candy must be used to produce a 10 pound mixture worth a total of $27.50? 46. Suppose Joe, working alone, can rake a certain lawn in 4 hours and that John, working alone, can rake the same lawn in 8 hours. How long would it take Joe and John working together to rake the same lawn? 47. A rectangular window has a length that is 8 inches more than its width. The perimeter of the window is 100 inches. Find the length and width of the window. 48. A car went 301 miles in 5 hours, traveling part of the time at 55 miles per hour and part of the time at 65 miles per hour. For what length of time did the car travel at each speed? Section 2.4 49. Solve for x and give the solution in interval notation:

€

−2(3x − 5) + 4 > 2x − 6 50. Solve for x and give the solution in interval notation:

€

−7 < −2x + 5 ≤11


51. Solve and give your solution in interval notation:

€

−1≤3x − 5

4< 7

52. The total cost y of producing x copies of a CD is given by

€

y = 2500 + 5x . For what number of CDs will the total cost be between $3,175 and $3,900? Section 2.5 53. Graph

€

y = 3x − 6 . 54. Solve:

€

4x − 5 = 7 55. Solve:

€

2x − 3 = −4 56. Solve:

€

3x − 4 = 5x + 9 57. Solve and give the solution in interval notation:

€

5x − 8 < 2 58. Solve and give the solution in interval notation:

€

2x − 5 ≥1 Answers 1. (a) integer, rational number (b) irrational number (c) rational number (d) rational number 2. (a) –144 (b) –18 3. (a)

€

3.95 ×10−4 (b)

€

5.43 ×104 4. (a) 0.000538 (b) 92,400 5.

€

4.2 ×10−2 6. 12% 7. 85 8. 86 9.

€

2 13 10.

€

1,−3( ) 11. (a)

€

−3,1,5{ } (b)

€

4,2,−6{ } 12.

€

(x +1)2 + ( y +1)2 = 9 13. (a)

€

7,−5( ) (b) 2

14.

€

x − 4( )2+ y + 3( )2

=169 15.

€

x − 2( )2+ y +1( )2

= 50 16. (a) Yes, because no first number in the ordered pairs is repeated as a first number. (b) No, because the graph fails the Vertical Line Test. (c) No, because 3 is repeated as a first number in the ordered pairs.

17. (a)

€

x x ≠ −5,5{ } (b)

€

x x is a real number{ } (c)

€

x x ≥23

⎧ ⎨ ⎩

⎫ ⎬ ⎭

18. (a) –4 (b) –11 (c)

€

−a2 − 4a +1 19. (a) F (b) T 20. (a)

€

x 0 ≤ x ≤ 3{ } (b) 3 (c) –3, –1, 3 21. (a) 7 (b) Carpet cost $7 per sq yd.


22.

€

[−3,5) 23.

€

(−∞,−1](2,∞) 24. (a)

€

(−∞,−1][3,4] (b)

€

[−1,3][4,∞) 25. –1 26. (a)

€

3x2 + 6hx + 3h2 − 5x − 5h + 4 (b)

€

6x + 3h − 5 27. (a) Yes

(b)

€

y =43

x + 2

28.

€

y = −23

x + 2

29. (a)

€

−32

(b) (4,0) (c) (0,6)

30. (a)

€

45

(b)

€

(−5,0) (c)

€

(0,4)

31. (a) 0 (b) none (c)

€

(0,−4)

32. (a) undefined (b)

€

(5,0) (c) none

33. (a) 4 (b) 0 (c)

34. (a)

€

y = 6x + 7 (b) 6 mph (c) 7 mi (d) 19 mi

35.

€

y = −32

x + 8 36.

€

y = −34

x + 4

37.

€

N (t ) = 8.2t +17.5 38. 4.9 million

39.

€

V (t ) = 4000x − 7,842,000 40.

€

1207

41. $660 42.

€

−45

43. –8 44.

€

3a − 85


45. 2.5 lb of Jelly Beans, 7.5 lb of Gummy Bears

46.

€

223

hr 47. Length: 29 in., Width: 21 in.

48. 2.4 hr at 55 mph, 2.6 hr at 65 mph

49.

€

−∞,52

⎛

⎝ ⎜

⎞

⎠ ⎟

50.

€

[−3,6)

51.

€

13

,11⎡

⎣ ⎢

⎞

⎠ ⎟

52. Between 135 and 280 CDs.

54.

€

−12

,3 55. No solution

56.

€

−58

,−132

57.

€

65

,2⎛

⎝ ⎜

⎞

⎠ ⎟

58.

€

−∞,2( ] 3,∞[ )

math 1314 - college algebra review for test 1 · math 1314 - college algebra review for test 1...

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