Question 1

Use synthetic division to find the function value.
-$f ( x ) = x ^ { 3 } + 11$; find $f ( 2 + i )$.

Accepted Answer

A)  $2 + 11 i$ 
B)  $2 + 12 \mathrm { i }$ 
C)  $13 + 12 \mathrm { i }$ 
D)  $13 + 11 \mathrm { i }$ 
A)  $2 + 11 i$ 
B)  $2 + 12 \mathrm { i }$ 
C)  $13 + 12 \mathrm { i }$ 
D)  $13 + 11 \mathrm { i }$

Question 2

Find a rational function that satisfies the given conditions. Answers may vary, but try to give the simplest answer
possible.
-Oblique asymptote $y = x + 5$

Accepted Answer

A)  $f ( x ) = \frac { x ^ { 2 } - 5 x + 1 } { 5 x }$ 
B)  $f ( x ) = \frac { x ^ { 2 } + 5 x + 1 } { x }$ 
C)  $f ( x ) = \frac { x ^ { 2 } + 5 x + 1 } { 5 x }$ 
D)  $f ( x ) = \frac { x ^ { 2 } - 5 x + 1 } { x }$ 
A)  $f ( x ) = \frac { x ^ { 2 } - 5 x + 1 } { 5 x }$ 
B)  $f ( x ) = \frac { x ^ { 2 } + 5 x + 1 } { x }$ 
C)  $f ( x ) = \frac { x ^ { 2 } + 5 x + 1 } { 5 x }$ 
D)  $f ( x ) = \frac { x ^ { 2 } - 5 x + 1 } { x }$

Question 3

Match the equation with the appropriate graph.
-$$f ( x ) = \frac { x ^ { 3 } } { x ^ { 2 } + 9 }$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 4

Given that the polynomial function has the given zero, find the other zeros.
-$$f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 8 x + 10 ; 1 + i$$

Accepted Answer

A)  $1 - \mathrm { i } , 5$ 
B)  $1 - \mathrm { i } , - 5$ 
C)  $1 - i , 5 i$ 
D)  $- 5,5$ 
A)  $1 - \mathrm { i } , 5$ 
B)  $1 - \mathrm { i } , - 5$ 
C)  $1 - i , 5 i$ 
D)  $- 5,5$

Question 5

Given that the polynomial function has the given zero, find the other zeros.
-$$f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 11 x + 52 ; - 4$$

Accepted Answer

A)  $3 + 4 \mathrm { i } , 3 - 4 \mathrm { i }$ 
B)  $3 + 2 i , 3 - 2 i$ 
C)  $1 + 2 \sqrt { 13 } i , 1 - 2 \sqrt { 13 } i$ 
D)  $1 + 2 i , 1 - 2 i$ 
A)  $3 + 4 \mathrm { i } , 3 - 4 \mathrm { i }$ 
B)  $3 + 2 i , 3 - 2 i$ 
C)  $1 + 2 \sqrt { 13 } i , 1 - 2 \sqrt { 13 } i$ 
D)  $1 + 2 i , 1 - 2 i$

Question 6

List the critical values of the related function. Then solve the inequality.
-$$\frac { 2 } { x ^ { 2 } + 1 } \geq \frac { 4 } { 4 x ^ { 2 } + 3 }$$

Accepted Answer

A)  No critical values; $( - \infty , \infty )$ 
B)  $2 ; ( - \infty , 2 ]$ 
C)  No critical values; $\varnothing$ 
D)  $4 ; [ 4 , \infty )$ 
A)  No critical values; $( - \infty , \infty )$ 
B)  $2 ; ( - \infty , 2 ]$ 
C)  No critical values; $\varnothing$ 
D)  $4 ; [ 4 , \infty )$

Question 7

Given the polynomial function f(x), find the rational zeros, then the other zeros (that is, solve the equation f(x) = 0), and
factor f(x) into linear factors.
-$$f ( x ) = \frac { 1 } { 2 } x ^ { 3 } - \frac { 2 } { 3 } x ^ { 2 } - \frac { 1 } { 12 } x + \frac { 1 } { 12 }$$

Accepted Answer

A)  $\frac { 1 } { 3 } , \frac { 1 + \sqrt { 3 } } { 2 } , \frac { 1 - \sqrt { 3 } } { 2 } ; f ( x ) = \left( x - \frac { 1 } { 3 } \right) \left( x - \frac { 1 + \sqrt { 3 } } { 2 } \right) \left( x - \frac { 1 - \sqrt { 3 } } { 2 } \right)$ 
B)  $\frac { 1 } { 2 } , \frac { 1 + \sqrt { 3 } } { 2 } , \frac { 1 - \sqrt { 3 } } { 2 } ; f ( x ) = \left( \frac { 1 } { 3 } \right) \left( x - \frac { 1 } { 3 } \right) \left( x - \frac { 1 + \sqrt { 3 } } { 2 } \right) \left( x - \frac { 1 - \sqrt { 3 } } { 2 } \right)$ 
C)  $\frac { 1 } { 2 } , \frac { 1 + \sqrt { 2 } } { 2 } , \frac { 1 - \sqrt { 2 } } { 2 } ; f ( x ) = \left( x - \frac { 1 } { 2 } \right) \left( x - \frac { 1 + \sqrt { 2 } } { 2 } \right) \left( x - \frac { 1 - \sqrt { 2 } } { 2 } \right)$ 
D)  $\frac { 1 } { 3 } , \frac { 1 + \sqrt { 3 } } { 2 } , \frac { 1 - \sqrt { 3 } } { 2 } ; f ( x ) = \left( \frac { 1 } { 2 } \right) \left( x - \frac { 1 } { 3 } \right) \left( x - \frac { 1 + \sqrt { 3 } } { 2 } \right) \left( x - \frac { 1 - \sqrt { 3 } } { 2 } \right)$ 
A)  $\frac { 1 } { 3 } , \frac { 1 + \sqrt { 3 } } { 2 } , \frac { 1 - \sqrt { 3 } } { 2 } ; f ( x ) = \left( x - \frac { 1 } { 3 } \right) \left( x - \frac { 1 + \sqrt { 3 } } { 2 } \right) \left( x - \frac { 1 - \sqrt { 3 } } { 2 } \right)$ 
B)  $\frac { 1 } { 2 } , \frac { 1 + \sqrt { 3 } } { 2 } , \frac { 1 - \sqrt { 3 } } { 2 } ; f ( x ) = \left( \frac { 1 } { 3 } \right) \left( x - \frac { 1 } { 3 } \right) \left( x - \frac { 1 + \sqrt { 3 } } { 2 } \right) \left( x - \frac { 1 - \sqrt { 3 } } { 2 } \right)$ 
C)  $\frac { 1 } { 2 } , \frac { 1 + \sqrt { 2 } } { 2 } , \frac { 1 - \sqrt { 2 } } { 2 } ; f ( x ) = \left( x - \frac { 1 } { 2 } \right) \left( x - \frac { 1 + \sqrt { 2 } } { 2 } \right) \left( x - \frac { 1 - \sqrt { 2 } } { 2 } \right)$ 
D)  $\frac { 1 } { 3 } , \frac { 1 + \sqrt { 3 } } { 2 } , \frac { 1 - \sqrt { 3 } } { 2 } ; f ( x ) = \left( \frac { 1 } { 2 } \right) \left( x - \frac { 1 } { 3 } \right) \left( x - \frac { 1 + \sqrt { 3 } } { 2 } \right) \left( x - \frac { 1 - \sqrt { 3 } } { 2 } \right)$

Question 8

Use long division to determine whether the binomial is a factor of f(x).
-$$f ( x ) = x ^ { 4 } - 10 x ^ { 3 } + 35 x ^ { 2 } - 50 x + 24 ; x - 2$$

Accepted Answer

A)  No 
B)  Yes 
A)  No 
B)  Yes

Question 9

Graph the function, showing all asymptotes (those that do not correspond to an axis) as dashed lines. List the x- and
y-intercepts.
-$$f ( x ) = \frac { x - 4 } { x + 5 }$$

Accepted Answer

A)  x-intercept: $( 4,0 ) ; y$-intercept: $\left( 0 , - \frac { 4 } { 5 } \right)$;
  
B)  x-intercept: $( 4,0 ) ; y$-intercept: $\left( 0 , \frac { 4 } { 5 } \right)$
  
C)  $x$-intercept: $( 4,0 ) ; y$-intercept: $\left( 0 , - \frac { 4 } { 5 } \right)$;
  
D)  $x$-intercept: $( 4,0 ) ; y$-intercept: $\left( 0 , \frac { 4 } { 5 } \right)$;
  
A)  x-intercept: $( 4,0 ) ; y$-intercept: $\left( 0 , - \frac { 4 } { 5 } \right)$;
  
B)  x-intercept: $( 4,0 ) ; y$-intercept: $\left( 0 , \frac { 4 } { 5 } \right)$
  
C)  $x$-intercept: $( 4,0 ) ; y$-intercept: $\left( 0 , - \frac { 4 } { 5 } \right)$;
  
D)  $x$-intercept: $( 4,0 ) ; y$-intercept: $\left( 0 , \frac { 4 } { 5 } \right)$;

Question 10

Solve.
-$$x ^ { 2 } + 6 < 2 x$$

Accepted Answer

A)  $\{ 2 \}$ 
B)  $\varnothing$ 
C)  $( - \infty , - 2 )$ 
D)  $( 2 , \infty )$ 
A)  $\{ 2 \}$ 
B)  $\varnothing$ 
C)  $( - \infty , - 2 )$ 
D)  $( 2 , \infty )$

Question 11

Graph the function.
-$$h ( x ) = x ^ { 5 } - 17 x ^ { 2 } + 16 x$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 12

Given that the polynomial function has the given zero, find the other zeros.
-$$f ( x ) = x ^ { 3 } - 64 ; 4$$

Accepted Answer

A)  $- 2 + \sqrt { 3 } i , - 2 - \sqrt { 3 } i$ 
B)  $- 2 + 2 \sqrt { 3 } i , - 2 - 2 \sqrt { 3 } i$ 
C)  $- 1 + 2 \sqrt { 3 } i , - 1 - 2 \sqrt { 3 } i$ 
D)  $- 2 + 4 \sqrt { 3 } i , - 2 - 4 \sqrt { 3 } i$ 
A)  $- 2 + \sqrt { 3 } i , - 2 - \sqrt { 3 } i$ 
B)  $- 2 + 2 \sqrt { 3 } i , - 2 - 2 \sqrt { 3 } i$ 
C)  $- 1 + 2 \sqrt { 3 } i , - 1 - 2 \sqrt { 3 } i$ 
D)  $- 2 + 4 \sqrt { 3 } i , - 2 - 4 \sqrt { 3 } i$

Question 13

Using synthetic division, determine whether the numbers are zeros of the polynomial.
-$$- 3,0 ; f ( x ) = - 4 x ^ { 3 } + x ^ { 2 } + 2 x + 7$$

Accepted Answer

A)  No; no 
B)  No; yes 
C)  Yes; no 
D)  Yes; yes 
A)  No; no 
B)  No; yes 
C)  Yes; no 
D)  Yes; yes

Question 14

State the domain of the rational function.
-$$f ( x ) = \frac { x ^ { 2 } + 4 x - 12 } { x ^ { 2 } - 2 x - 8 }$$

Accepted Answer

A)  $( - \infty , - 4 ) \cup ( - 4,2 ) \cup ( 2 , \infty )$ 
B)  $( - \infty , - 2 ) \cup ( - 2,4 ) \cup ( 4 , \infty )$ 
C)  $( - \infty , \infty )$ 
D)  $( - \infty , 4 ) \cup ( 4 , \infty )$ 
A)  $( - \infty , - 4 ) \cup ( - 4,2 ) \cup ( 2 , \infty )$ 
B)  $( - \infty , - 2 ) \cup ( - 2,4 ) \cup ( 4 , \infty )$ 
C)  $( - \infty , \infty )$ 
D)  $( - \infty , 4 ) \cup ( 4 , \infty )$

Question 15

Find only the rational zeros.
-$$f ( x ) = x ^ { 5 } - 5 x ^ { 4 } + 5 x ^ { 3 } + 15 x ^ { 2 } - 36 x + 20$$

Accepted Answer

A)  $- 1,2 , - 2$ 
B)  $1,2,3$ 
C)  $1,2 , - 2$ 
D)  No rational zeros 
A)  $- 1,2 , - 2$ 
B)  $1,2,3$ 
C)  $1,2 , - 2$ 
D)  No rational zeros

Question 16

Find the zeros of the polynomial function and state the multiplicity of each.
-$$f ( x ) = x ^ { 3 } + 8 x ^ { 2 } - x - 8$$

Accepted Answer

A)  $- 1$, multiplicity $1 ; 1$, multiplicity $1 ; 8$, multiplicity 1 
B)  $- 8$, multiplicity $2 ; 1$, multiplicity 1 
C)  $- 8$, multiplicity $1 ; - 1$, multiplicity $1 ; 1$, multiplicity 1 
D)  $- 8$, multiplicity $1 ; - 1$, multiplicity 2 
A)  $- 1$, multiplicity $1 ; 1$, multiplicity $1 ; 8$, multiplicity 1 
B)  $- 8$, multiplicity $2 ; 1$, multiplicity 1 
C)  $- 8$, multiplicity $1 ; - 1$, multiplicity $1 ; 1$, multiplicity 1 
D)  $- 8$, multiplicity $1 ; - 1$, multiplicity 2

Question 17

Solve.
-The average cost per tape, in dollars, for a company to produce x sports videotapes is given by the function $$A ( x ) = \frac { 14 x + 80 } { x } \text { for } x > 0$$
Graph the function on the interval $( 0 , \infty )$ and complete the following:
$$\mathrm { A } ( \mathrm { x } ) \rightarrowــــــــــ \quad \text { as } \mathrm { x } \rightarrow \infty \text {. }$$

Accepted Answer

A) 
 
$\mathrm { A } ( \mathrm { x } ) \rightarrow 1$ as $\mathrm { x } \rightarrow \infty$. 
B)

$\mathrm { A } ( \mathrm { x } ) \rightarrow 0$ as $\mathrm { x } \rightarrow \infty .$ 
C) 
 
$\mathrm { A } ( \mathrm { x } ) \rightarrow 19$ as $\mathrm { x } \rightarrow \infty .$ 
D) 
 
$\mathrm { A } ( \mathrm { x } ) \rightarrow 14$ as $\mathrm { x } \rightarrow \infty$. 
A) 
 
$\mathrm { A } ( \mathrm { x } ) \rightarrow 1$ as $\mathrm { x } \rightarrow \infty$. 
B)

$\mathrm { A } ( \mathrm { x } ) \rightarrow 0$ as $\mathrm { x } \rightarrow \infty .$ 
C) 
 
$\mathrm { A } ( \mathrm { x } ) \rightarrow 19$ as $\mathrm { x } \rightarrow \infty .$ 
D) 
 
$\mathrm { A } ( \mathrm { x } ) \rightarrow 14$ as $\mathrm { x } \rightarrow \infty$.

Question 18

Given that the polynomial function has the given zero, find the other zeros.
-$$f ( x ) = x ^ { 4 } - 21 x ^ { 2 } - 100 ; - 2 i$$

Accepted Answer

A)  $2 \mathrm { i } , 5 \mathrm { i } , - 5 \mathrm { i }$ 
B)  $2 \mathrm { i } , 10 , - 10$ 
C)  $2 \mathrm { i } , 5 , - 5$ 
D)  $2 \mathrm { i } , 10 \mathrm { i } , - 10 \mathrm { i }$ 
A)  $2 \mathrm { i } , 5 \mathrm { i } , - 5 \mathrm { i }$ 
B)  $2 \mathrm { i } , 10 , - 10$ 
C)  $2 \mathrm { i } , 5 , - 5$ 
D)  $2 \mathrm { i } , 10 \mathrm { i } , - 10 \mathrm { i }$

Question 19

Solve.
-The population $\mathrm { P }$, in thousands, of Pine Grove is given by $\mathrm { P } ( \mathrm { t } ) = \frac { 600 \mathrm { t } } { 2 \mathrm { t } ^ { 2 } + 9 }$, where $t$ is the time, in months. Find the interval on which the population was 40 thousand or greater.

Accepted Answer

A)  $[ 0.526,5.474 ]$ 
B)  $( - \infty , \infty )$ 
C)  $[ 0.658,6.842 ]$ 
D)  $[ 5.474 , \infty )$ 
A)  $[ 0.526,5.474 ]$ 
B)  $( - \infty , \infty )$ 
C)  $[ 0.658,6.842 ]$ 
D)  $[ 5.474 , \infty )$

Question 20

Use the leading-term test to match the function with the correct graph.
-$$f ( x ) = x ^ { 4 } - 4 x ^ { 3 } + 15 x ^ { 2 } + x - 14$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Use synthetic division to find the function value. - $f ( x ) = x ^ { 3 } + 11$ ; find $f ( 2 + i )$ .

Find a rational function that satisfies the given conditions. Answers may vary, but try to give the simplest answer possible. -Oblique asymptote $y = x + 5$

Match the equation with the appropriate graph. - $f ( x ) = \frac { x ^ { 3 } } { x ^ { 2 } + 9 }$

Given that the polynomial function has the given zero, find the other zeros. - $f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 8 x + 10 ; 1 + i$

Given that the polynomial function has the given zero, find the other zeros. - $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 11 x + 52 ; - 4$

List the critical values of the related function. Then solve the inequality. - $\frac { 2 } { x ^ { 2 } + 1 } \geq \frac { 4 } { 4 x ^ { 2 } + 3 }$

Given the polynomial function f(x), find the rational zeros, then the other zeros (that is, solve the equation f(x) = 0), and factor f(x) into linear factors. - $f ( x ) = \frac { 1 } { 2 } x ^ { 3 } - \frac { 2 } { 3 } x ^ { 2 } - \frac { 1 } { 12 } x + \frac { 1 } { 12 }$

Use long division to determine whether the binomial is a factor of f(x). - $f ( x ) = x ^ { 4 } - 10 x ^ { 3 } + 35 x ^ { 2 } - 50 x + 24 ; x - 2$

Solve. - $x ^ { 2 } + 6 < 2 x$

Graph the function. - $h ( x ) = x ^ { 5 } - 17 x ^ { 2 } + 16 x$ $Graph the function. - h ( x ) = x ^ { 5 } - 17 x ^ { 2 } + 16 x$

Given that the polynomial function has the given zero, find the other zeros. - $f ( x ) = x ^ { 3 } - 64 ; 4$

Using synthetic division, determine whether the numbers are zeros of the polynomial. - $- 3,0 ; f ( x ) = - 4 x ^ { 3 } + x ^ { 2 } + 2 x + 7$

State the domain of the rational function. - $f ( x ) = \frac { x ^ { 2 } + 4 x - 12 } { x ^ { 2 } - 2 x - 8 }$

Find only the rational zeros. - $f ( x ) = x ^ { 5 } - 5 x ^ { 4 } + 5 x ^ { 3 } + 15 x ^ { 2 } - 36 x + 20$

Find the zeros of the polynomial function and state the multiplicity of each. - $f ( x ) = x ^ { 3 } + 8 x ^ { 2 } - x - 8$

Given that the polynomial function has the given zero, find the other zeros. - $f ( x ) = x ^ { 4 } - 21 x ^ { 2 } - 100 ; - 2 i$

Solve. -The population $\mathrm { P }$ , in thousands, of Pine Grove is given by $\mathrm { P } ( \mathrm { t } ) = \frac { 600 \mathrm { t } } { 2 \mathrm { t } ^ { 2 } + 9 }$ , where $t$ is the time, in months. Find the interval on which the population was 40 thousand or greater.

Use the leading-term test to match the function with the correct graph. - $f ( x ) = x ^ { 4 } - 4 x ^ { 3 } + 15 x ^ { 2 } + x - 14$

Graphs, Functions, and Models

More on Functions

Quadratic Functions and Equations; Inequalities

Exponential and Logarithmic Functions

Systems of Equations and Matrices

Conic Sections

Sequences, Series, and Combinatorics

Filters

Exam 4: Polynomial and Rational Functions

Use synthetic division to find the function value. - f(x)=x3+11f ( x ) = x ^ { 3 } + 11f(x)=x3+11 ; find f(2+i)f ( 2 + i )f(2+i) .

Find a rational function that satisfies the given conditions. Answers may vary, but try to give the simplest answer possible. -Oblique asymptote y=x+5y = x + 5y=x+5

Match the equation with the appropriate graph. - f(x)=x3x2+9f ( x ) = \frac { x ^ { 3 } } { x ^ { 2 } + 9 }f(x)=x2+9x3​

Given that the polynomial function has the given zero, find the other zeros. - f(x)=x3+3x2−8x+10;1+if ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 8 x + 10 ; 1 + if(x)=x3+3x2−8x+10;1+i

Given that the polynomial function has the given zero, find the other zeros. - f(x)=x3−2x2−11x+52;−4f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 11 x + 52 ; - 4f(x)=x3−2x2−11x+52;−4

List the critical values of the related function. Then solve the inequality. - 2x2+1≥44x2+3\frac { 2 } { x ^ { 2 } + 1 } \geq \frac { 4 } { 4 x ^ { 2 } + 3 }x2+12​≥4x2+34​

Use long division to determine whether the binomial is a factor of f(x). - f(x)=x4−10x3+35x2−50x+24;x−2f ( x ) = x ^ { 4 } - 10 x ^ { 3 } + 35 x ^ { 2 } - 50 x + 24 ; x - 2f(x)=x4−10x3+35x2−50x+24;x−2

Graph the function, showing all asymptotes (those that do not correspond to an axis) as dashed lines. List the x- and y-intercepts. - f(x)=x−4x+5f ( x ) = \frac { x - 4 } { x + 5 }f(x)=x+5x−4​

Solve. - x2+6<2xx ^ { 2 } + 6 < 2 xx2+6<2x

Graph the function. - h(x)=x5−17x2+16xh ( x ) = x ^ { 5 } - 17 x ^ { 2 } + 16 xh(x)=x5−17x2+16x

Given that the polynomial function has the given zero, find the other zeros. - f(x)=x3−64;4f ( x ) = x ^ { 3 } - 64 ; 4f(x)=x3−64;4

Using synthetic division, determine whether the numbers are zeros of the polynomial. - −3,0;f(x)=−4x3+x2+2x+7- 3,0 ; f ( x ) = - 4 x ^ { 3 } + x ^ { 2 } + 2 x + 7−3,0;f(x)=−4x3+x2+2x+7

State the domain of the rational function. - f(x)=x2+4x−12x2−2x−8f ( x ) = \frac { x ^ { 2 } + 4 x - 12 } { x ^ { 2 } - 2 x - 8 }f(x)=x2−2x−8x2+4x−12​

Find only the rational zeros. - f(x)=x5−5x4+5x3+15x2−36x+20f ( x ) = x ^ { 5 } - 5 x ^ { 4 } + 5 x ^ { 3 } + 15 x ^ { 2 } - 36 x + 20f(x)=x5−5x4+5x3+15x2−36x+20

Find the zeros of the polynomial function and state the multiplicity of each. - f(x)=x3+8x2−x−8f ( x ) = x ^ { 3 } + 8 x ^ { 2 } - x - 8f(x)=x3+8x2−x−8

Given that the polynomial function has the given zero, find the other zeros. - f(x)=x4−21x2−100;−2if ( x ) = x ^ { 4 } - 21 x ^ { 2 } - 100 ; - 2 if(x)=x4−21x2−100;−2i

Use the leading-term test to match the function with the correct graph. - f(x)=x4−4x3+15x2+x−14f ( x ) = x ^ { 4 } - 4 x ^ { 3 } + 15 x ^ { 2 } + x - 14f(x)=x4−4x3+15x2+x−14

Graphs, Functions, and Models

More on Functions

Quadratic Functions and Equations; Inequalities

Exponential and Logarithmic Functions

Systems of Equations and Matrices

Conic Sections

Sequences, Series, and Combinatorics

Filters

Use synthetic division to find the function value. - $f ( x ) = x ^ { 3 } + 11$ ; find $f ( 2 + i )$ .

Find a rational function that satisfies the given conditions. Answers may vary, but try to give the simplest answer possible. -Oblique asymptote $y = x + 5$

Match the equation with the appropriate graph. - $f ( x ) = \frac { x ^ { 3 } } { x ^ { 2 } + 9 }$

Given that the polynomial function has the given zero, find the other zeros. - $f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 8 x + 10 ; 1 + i$

Given that the polynomial function has the given zero, find the other zeros. - $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 11 x + 52 ; - 4$

List the critical values of the related function. Then solve the inequality. - $\frac { 2 } { x ^ { 2 } + 1 } \geq \frac { 4 } { 4 x ^ { 2 } + 3 }$

Use long division to determine whether the binomial is a factor of f(x). - $f ( x ) = x ^ { 4 } - 10 x ^ { 3 } + 35 x ^ { 2 } - 50 x + 24 ; x - 2$

Solve. - $x ^ { 2 } + 6 < 2 x$

Graph the function. - $h ( x ) = x ^ { 5 } - 17 x ^ { 2 } + 16 x$ $Graph the function. - h ( x ) = x ^ { 5 } - 17 x ^ { 2 } + 16 x$

Given that the polynomial function has the given zero, find the other zeros. - $f ( x ) = x ^ { 3 } - 64 ; 4$

Using synthetic division, determine whether the numbers are zeros of the polynomial. - $- 3,0 ; f ( x ) = - 4 x ^ { 3 } + x ^ { 2 } + 2 x + 7$

State the domain of the rational function. - $f ( x ) = \frac { x ^ { 2 } + 4 x - 12 } { x ^ { 2 } - 2 x - 8 }$

Find only the rational zeros. - $f ( x ) = x ^ { 5 } - 5 x ^ { 4 } + 5 x ^ { 3 } + 15 x ^ { 2 } - 36 x + 20$

Find the zeros of the polynomial function and state the multiplicity of each. - $f ( x ) = x ^ { 3 } + 8 x ^ { 2 } - x - 8$

Given that the polynomial function has the given zero, find the other zeros. - $f ( x ) = x ^ { 4 } - 21 x ^ { 2 } - 100 ; - 2 i$

Use the leading-term test to match the function with the correct graph. - $f ( x ) = x ^ { 4 } - 4 x ^ { 3 } + 15 x ^ { 2 } + x - 14$