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AP Precalculus Unit 1: Polynomial and Rational Functions

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Unit 1: Polynomial and Rational Functions

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Question 1

What is the degree of the polynomial $f (x) = 3 x^{4} - 2 x^{3} + 5 x - 7$ ?

3

4

5

7

Question 2

The polynomial $f (x) = (x - 2)^{2} (x + 1)$ has a zero at $x = 2$ . Which best describes the graph of $f$ at $x = 2$ ?

A.Crosses the

x

-axis at

x = 2

.B.Touches the

x

-axis and turns around at

x = 2

.C.Has a vertical asymptote at

x = 2

.D.Is undefined at

x = 2

Question 3

What is the horizontal asymptote of $f (x) = \frac{3 x ^{2} + 7}{2 x ^{2} - x + 5}$ ?

y = 0

y = \frac{2}{3}

y = \frac{3}{2}

D.No horizontal asymptote.

Question 4

Which best describes the behavior of $f (x) = \frac{x ^{2} - 1}{x - 1}$ at $x = 1$ ?

A.Vertical asymptote at

x = 1

.B.Hole (removable discontinuity) at

x = 1

.C.

x

-intercept at

x = 1

.D.Horizontal asymptote at

x = 1

Question 5

A polynomial $f (x)$ has degree $3$ , real coefficients, and zeros at $x = - 2$ , $x = 1$ , and $x = 4$ . If $f (0) = 16$ , what is $f (x)$ ?

f (x) = (x + 2) (x - 1) (x - 4)

f (x) = 2 (x + 2) (x - 1) (x - 4)

f (x) = (x - 2) (x + 1) (x + 4)

f (x) = 4 (x + 2) (x - 1) (x - 4)

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Question 6

A linear function $g$ has constant rate of change $2$ , and a quadratic function $q (x) = x^{2}$ has rate of change that varies with $x$ . Over the interval $[1, 5]$ , what is the average rate of change of $q$ , and how does it compare to $g$ 's rate?

A.Average rate of

q

4

; faster than

g

's rate.B.Average rate of

q

6

; faster than

g

's rate.C.Average rate of

q

6

; slower than

g

's rate.D.Average rate of

q

24

; faster than

g

's rate.

Question 7

What are the real zeros of $f (x) = x^{2} - 9$ ?

x = 3

onlyB.

x = \pm 3

x = \pm 9

x = 0

Question 8

Let $f (x) = \frac{2 x ^{2} + 3 x + 1}{x ^{2} - 1}$ . Identify all asymptotes and any holes.

A.Vertical asymptotes at

x = \pm 1

; horizontal asymptote

y = 2

.B.Hole at

x = - 1

; vertical asymptote

x = 1

; horizontal asymptote

y = 2

.C.Hole at

x = 1

; vertical asymptote

x = - 1

; horizontal asymptote

y = 2

.D.Vertical asymptotes at

x = \pm 1

; no horizontal asymptote.

Question 9

As $x \to \infty$ , what is the end behavior of $f (x) = - 2 x^{3} + 5 x^{2} - x + 4$ ?

f (x) \to \infty

f (x) \to - \infty

f (x) \to 4

f (x) \to 0

Question 10

Find the quotient when $f (x) = x^{3} + 2 x^{2} - 5 x - 6$ is divided by $x - 2$ .

x^{2} + 4 x + 3

x^{2} - 4 x + 3

x^{2} + 2 x - 3

x^{2} + 4 x + 5

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Question 11

What is the zero of the linear function $f (x) = 2 x - 8$ ?

x = - 4

x = - 8

x = 4

x = 8

Question 12

Identify the vertical asymptote(s) of $f (x) = \frac{x + 3}{x ^{2} - 4}$ .

x = - 3

onlyB.

x = 2

onlyC.

x = 2

and

x = - 2

x = \pm 3

AP Precalculus Unit 1: Polynomial and Rational Functions — Free with Answer Explanations | Test Practice Hub