Free Printable Unit 2 Review: Polynomial and Rational Functions

1.

Which of the following gives the same solutions as x² - 18 = -3x?

a)

(x - 3)(x + 6) = 0

b)

(x + 3)(x - 6) = 0

c)

(x - 2)(x + 9) = 0

d)

(x + 2)(x - 9) = 0

2.

Expand the first three terms of the binomial: $\left(x-3y\right)^7$

a)

$x^7-21x^6+63x^5y^2-...$

b)

$x^7-21x^6y+189x^5y^2-...$

c)

$x^7-21x^6y+147x^5y^2-...$

d)

$x^7-21x^6y+84x^5y^2-...$

3.

Find the end behavior of $f\left(x\right)=-2x^3+5x^4$ .

a)

$\lim_{x\rightarrow-\infty}f\left(x\right)=+\infty$ and $\lim_{x\rightarrow+\infty}f\left(x\right)=-\infty$

b)

$\lim_{x\rightarrow-\infty}f\left(x\right)=-\infty$ and $\lim_{x\rightarrow+\infty}f\left(x\right)=+\infty$

c)

$\lim_{x\rightarrow\pm\infty}f\left(x\right)=-\infty$

d)

$\lim_{x\rightarrow\pm\infty}f\left(x\right)=+\infty$

4.

Classify the number and type of roots of $f\left(x\right)=x^6-2x^4-16x^2+32$ .

a)

6 rational roots

b)

4 rational and 2 irrational roots

c)

4 irrational and 2 imaginary roots

d)

2 rational, 2 irrational, and 2 imaginary roots

5.

The graph below is the graph of g(x). Write g(x) as a product of linear factors.

a)

$g\left(x\right)=x\left(x+3\right)\left(x-1\right)$

b)

$g\left(x\right)=x\left(x-3\right)\left(x+1\right)$

c)

$g\left(x\right)=\left(x+3\right)\left(x-1\right)$

d)

$g\left(x\right)=\left(x-3\right)\left(x+1\right)$

6.

Divide: $\frac{x^4-5x^3+25x-21}{x-3}$

a)

$x^3-2x^2-6x+19+\frac{2}{x-3}$

b)

$x^3+4x^2+12x-11-\frac{12}{x-3}$

c)

$x^3-2x^2-6x+7$

d)

$x^3-2x^2+19x+7$

7.

$f\left(x\right)=x^5-10x^2-x+10.\ \ \$ Which of the following is not a root of f(x)?

a)

$-1+2i$

b)

$1+2i$

c)

$-1$

d)

$1$

8.

For which of the following values of k will $g\left(x\right)=\frac{kx+6}{4x-5}$ have an end behavior of $\lim_{x\rightarrow\pm\infty}g\left(x\right)=3$ ?

a)

k = 18

b)

k = 12

c)

k = 2

d)

k = 3

9.

Which of the following occurs in the graph of $y=\frac{2x^2-8}{x-2}$ at x = 2?

a)

A vertical asymptote at x = 2

b)

The defined point (2, 4)

c)

A point of discontinuity at (2, 0)

d)

A point of discontinuity at (2, 8)

10.

Find the equations of the vertical asymptotes of $y=\frac{x\left(x-1\right)}{x^2+2x-3}$ .

a)

$x=-3$ and $x=1$

b)

$x=-3$ only

c)

$x=3$ and $x=-1$

d)

$x=3$ only

11.

Find the domain of $y=\frac{x-4}{x^2-4}$ .

a)

$\left(-\infty,\ 0\right)\cup\left(0,\ +\infty\right)$

b)

$\left(-\infty,\ 4\right)\cup\left(4,\ +\infty\right)$

c)

$\left(-\infty,\ -2\right)\cup\left(-2,\ 2\right)\cup\left(2,\ +\infty\right)$

d)

$\left(-\infty,\ 2\right)\ \cup\ \left(2,\ +\infty\right)$

12.

What is the equation of the slant asymptote of the function $h\left(x\right)=\frac{x^2+9x+28}{x+5}$ ?

a)

$y=x-5$

b)

$y=x+4$

c)

$y=x+3$

d)

$y=x-4$

Unit 2 Review: Polynomial and Rational Functions

Total questions: 12

Worksheet time: 6mins

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