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MATHEMATICS II I Advanced Algebra & Trigonometry

Second Term Exam SY 2014-2015

Name: _____________________________________ Section: _____ Date: Dec. , 2014 Score: I. TRUE or FALSE. Write the word TRUE if the statement is true and FALSE if otherwise. Write your answer on the space provided. ( 4 points)

______1) If functions f and g are inverses of each other, then, both functions are one-to-one.

______2) A one-to-one function should satisfy the horizontal line test.

______3) In the function f ( x )=√3−x , f (−6 )=√−3 .

______4)

g ( x )=2 x is the inverse of f ( x )= x

2.

II Multiple Choice. Encircle the letter of your answer.

1) Which of the following functions has range ?

I. II. III.

A) I only C) I and II only

B) II D) II and III only

2) Which of the following is TRUE for the function ?

I. The lowest point of the graph is .

II. The range of the function is .

III. The function has one x-intercept.

A) I only C) II and III only

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B) I and II only D) I, II and III

3) Which statements is / are TRUE about the graph of f ( x )=−|x+2|+3 ?

I. Its vertex is at (−2 , 3 ) .

II. It opens down.

III. It is wider than the graph of f ( x )=|x|

A) I and II only C) II and III only

B) II and III only D) I, II and III

4) Which of the following functions will NOT cross the x-axis?

I. II. III.

A) I only C) I and II only

B) II only D) I, II, and III

5) What is the remainder if P ( x )=2x16−3x11−4 is divided by x+1?

A) 1 C) 3

B) 2 D) 4

6) What is the value of k so that x−3 is a factor of P ( x )=2x3−5 x2+kx−15 ?

A) −38 C) 2

B) −8 D) 6

7) If P ( x )=3 x3+2 x2+x−10 , which pair of numbers is a possible rational zero of P ( x )?

A) ±3 C) ± 1

10

B) ±1

5 D) ±2

3

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8) Which of the following functions will have a domain of all real numbers?

I. f ( x )=x III. f ( x )= (x+2 )2−1

II. f ( x )=|x+2| IV. f ( x )=x3−2 x2+x−1

A) I and II only C) III and IV onlyB) II and III only D) I, II, III and IV

9) How many times will the graph of P ( x )=( x+1 ) (2 x+3 ) (x−2 ) cross the x-axis?

A) once C) thrice

B) twice D) four times

10) If f ( x )= x+5

x−2 , what is the domain of f ( x ) ?

A) { x|x ε ℜ , x≠−2 } C) { x|x ε ℜ , x≠5 }

B) { x|x ε ℜ , x≠2 } D) { x|x ε ℜ , x≠−5 and 2 }

11) Which of the following is the graph of f ( x )=2|x−3|+1?

A) C)

B) D)

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12) Which of the following is the equation of the graph of the function on the right side?

A) f ( x )=−√x−1 C) f ( x )=−√x+1

B) f ( x )=−√1−x D) f ( x )=−√−1−x

13) Which of the following is NOT a one-to-one function?

A) f ( x )=x C) f ( x )=√x+3

B) f ( x )=|x| D) f ( x )=x2−1 , x≥0

14) Let f and g be inverses of each other. Which of the following statements is/are FALSE?

I. If f is one-to-one, then g is also one-to-one.

II. The domain of f is the range of g .

III.f ( g ( x ) )=x andg (f ( x ) )=x .

IV.If f (b )=a , then g contains the point (a , b ) .

A) I and II only C) I, II, and III only

B) II and III only D) All four statements are true.

III. Solving: SHOW all necessary solutions and write your answer on the BOX provided.

1) If f ( x )=2 x3+3 x2−x+5 and g ( x )=x2−x+3 , find ( f⋅g ) ( x ) . ( 2 points)

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Answer:

2) Find the inverse of f ( x )=2 x−1

x+4 . ( 2 points)

3) If and , which has a greater a greater value, or

? Explain your answer by showing your solution .

( 2 points)

4) Find an equation of an absolute value function with vertex (4 , −2 ) and passes through point (0 ,−6 )

( 2 points)

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Answer:

Answer:

Answer:

5) Given the function P ( x )=x3−2x2−5x+6 , find

a) the possible rational zeros of the function . ( 1 point)

b) the roots of the function ( 3 points)

6) Jane supplies balloons for parties. The manufacturer charges her 50 cents wholesale for each balloon.

Jane then charges her customers one peso above what she pays for each balloon. Write a function f(x),

for the price Jane pays and a function, g(x), for the price she charges her customers. ( 2 points)

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Answer:

ROOTS:

f(x) =

g(x)

7) Give your own examples of the a square root function with the lowest point in quadrant III and goes

to the right direction. Find the inverse of your function and graph both functions in the same

rectangular plane. Identify 3 points of each graph. ( 4 points = 1 pt. for the square root function,

1 pt. for the inverse, 1 pt. for the graph and 1pt. for identifying the points in your graphs.)

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END of the TEST….. MERRY CHRISTMAS and a HAPPY NEW YEAR !!!

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