Question 1

Find the y-intercept of the polynomial function.
-

Accepted Answer

A)  origin symmetry 
B)  $\mathrm { y }$-axis symmetry 
C)  neither 
A)  origin symmetry 
B)  $\mathrm { y }$-axis symmetry 
C)  neither

Question 2

Graph the polynomial function.
-$f(x)=4 x^{2}-x^{3}$

Accepted Answer

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

Question 3

Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for the given
function.
-$$f ( x ) = x ^ { 5 } - 3.2 x ^ { 4 } - 19.58 x ^ { 3 } + 3 x ^ { 2 } + 49.21 x - 13.538$$

Accepted Answer

A)  3 or 1 positive zeros, 2 or 0 negative zeros 
B)  2 or 0 positive zeros, 2 or 0 negative zeros 
C)  3 or 1 positive zeros, 3 or 1 negative zeros 
D)  2 or 0 positive zeros, 3 or 1 negative zeros 
A)  3 or 1 positive zeros, 2 or 0 negative zeros 
B)  2 or 0 positive zeros, 2 or 0 negative zeros 
C)  3 or 1 positive zeros, 3 or 1 negative zeros 
D)  2 or 0 positive zeros, 3 or 1 negative zeros

Question 4

Use synthetic division to show that the number given to the right of the equation is a solution of the equation, then solve the polynomial equation.
-$$3 x ^ { 3 } + 8 x ^ { 2 } - 13 x - 30 = 0 ; - 3$$

Accepted Answer

A)  $\left\{ - \frac { 5 } { 3 } , 2 , - 3 \right\}$ 
B)  $\left\{ \frac { 5 } { 3 } , 2 , - 3 \right\}$ 
C)  $\left\{ - \frac { 5 } { 3 } , - 2 , - 3 \right\}$ 
D)  $\left\{ \frac { 2 } { 3 } , - 5 , - 3 \right\}$ 
A)  $\left\{ - \frac { 5 } { 3 } , 2 , - 3 \right\}$ 
B)  $\left\{ \frac { 5 } { 3 } , 2 , - 3 \right\}$ 
C)  $\left\{ - \frac { 5 } { 3 } , - 2 , - 3 \right\}$ 
D)  $\left\{ \frac { 2 } { 3 } , - 5 , - 3 \right\}$

Question 5

Graph the polynomial function.
-$f(x)=\frac{1}{4}-\frac{1}{4} x^{4}$

Accepted Answer

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

Question 6

Divide using long division.
-The width of a rectangle is $x - \frac { 1 } { 3 }$ feet and its area is $3 x ^ { 3 } + 17 x ^ { 2 } + 21 x - 9$ square feet. Write a polynomial that represents the length of the rectangle.

Accepted Answer

A)  $3 x ^ { 2 } + 18 x + 27 \mathrm { ft }$ 
B)  $3 \mathrm { x } ^ { 2 } - 18 \mathrm { x } + 27 \mathrm { ft }$ 
C)  $3 x ^ { 2 } + 16 x + \frac { 47 } { 3 } \mathrm { ft }$ 
D)  $3 x ^ { 2 } + 18 x - 27 f t$ 
A)  $3 x ^ { 2 } + 18 x + 27 \mathrm { ft }$ 
B)  $3 \mathrm { x } ^ { 2 } - 18 \mathrm { x } + 27 \mathrm { ft }$ 
C)  $3 x ^ { 2 } + 16 x + \frac { 47 } { 3 } \mathrm { ft }$ 
D)  $3 x ^ { 2 } + 18 x - 27 f t$

Question 7

Graph the polynomial function.
-$$f ( x ) = - 2 x ^ { 3 } ( x - 2 ) ^ { 2 } ( x - 1 )$$

Accepted Answer

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

Question 8

Find the domain of the rational function.
-$$h ( x ) = \frac { x + 4 } { x ^ { 2 } - 64 }$$

Accepted Answer

A)  $\{ x \mid x \neq - 8 , x \neq 8 \}$ 
B)  $\{ x \mid x \neq - 8 , x \neq 8 , x \neq - 4 \}$ 
C)  $\{ x \mid x \neq 0 , x \neq 64 \}$ 
D)  all real numbers 
A)  $\{ x \mid x \neq - 8 , x \neq 8 \}$ 
B)  $\{ x \mid x \neq - 8 , x \neq 8 , x \neq - 4 \}$ 
C)  $\{ x \mid x \neq 0 , x \neq 64 \}$ 
D)  all real numbers

Question 9

Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for the given
function.
-$$f ( x ) = 9 x ^ { 3 } - 7 x ^ { 2 } + x + 4.5$$

Accepted Answer

A)  2 or 0 positive zeros, 1 negative zero 
B)  3 or 1 positive zeros, 1 negative zero 
C)  2 or 0 positive zeros, no negative zeros 
D)  3 or 1 positive zeros, 2 or 0 negative zeros 
A)  2 or 0 positive zeros, 1 negative zero 
B)  3 or 1 positive zeros, 1 negative zero 
C)  2 or 0 positive zeros, no negative zeros 
D)  3 or 1 positive zeros, 2 or 0 negative zeros

Question 10

Graph the polynomial function.
-$f(x)=(x-3)(x-2)(x+1)^{2}$

Accepted Answer

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

Question 11

Graph the rational function.
-$f(x)=\frac{4}{x^{2}+10 x+25}$

Accepted Answer

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

Question 12

Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational
roots.
-$$x ^ { 4 } + 5 x ^ { 3 } - 2 x ^ { 2 } - 18 x - 12 = 0$$

Accepted Answer

A)  $\{ - 1,2 , - 3 + \sqrt { 3 } , - 3 - \sqrt { 3 } \}$ 
B)  $\{ 1 , - 2 , - 3 + \sqrt { 3 } , - 3 - \sqrt { 3 } \}$ 
C)  $\{ - 1,3 , - 3 + \sqrt { 5 } , - 3 - \sqrt { 5 } \}$ 
D)  $\{ - 1 , - 2 , - 3 + \sqrt { 5 } , - 3 - \sqrt { 5 } \}$ 
A)  $\{ - 1,2 , - 3 + \sqrt { 3 } , - 3 - \sqrt { 3 } \}$ 
B)  $\{ 1 , - 2 , - 3 + \sqrt { 3 } , - 3 - \sqrt { 3 } \}$ 
C)  $\{ - 1,3 , - 3 + \sqrt { 5 } , - 3 - \sqrt { 5 } \}$ 
D)  $\{ - 1 , - 2 , - 3 + \sqrt { 5 } , - 3 - \sqrt { 5 } \}$

Question 13

Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for the given
function.
-$$f ( x ) = - 7 x ^ { 9 } + x ^ { 7 } - x ^ { 2 } + 3$$

Accepted Answer

A)  3 or 1 positive zeros, 2 or 0 negative zeros 
B)  3 or 1 positive zeros, 3 or 1 negative zeros 
C)  2 or 0 positive zeros, 2 or 0 negative zeros 
D)  2 or 0 positive zeros, 3 or 1 negative zeros 
A)  3 or 1 positive zeros, 2 or 0 negative zeros 
B)  3 or 1 positive zeros, 3 or 1 negative zeros 
C)  2 or 0 positive zeros, 2 or 0 negative zeros 
D)  2 or 0 positive zeros, 3 or 1 negative zeros

Question 14

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end
-$$f ( x ) = - 3 x ^ { 4 } + 2 x ^ { 3 } + 5 x ^ { 2 } - 5 x - 2$$

Accepted Answer

A)  falls to the left and falls to the right 
B)  rises to the left and falls to the right 
C)  falls to the left and rises to the right 
D)  rises to the left and rises to the right 
A)  falls to the left and falls to the right 
B)  rises to the left and falls to the right 
C)  falls to the left and rises to the right 
D)  rises to the left and rises to the right

Question 15

Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.
-$$x ^ { 4 } + 2 x ^ { 3 } - 63 x ^ { 2 } = 0$$

Accepted Answer

A)  0 , touches the $x$-axis and turns around;
$- 9$, crosses the $x$-axis;
7 , crosses the $x$-axis 
B)  0 , touches the $x$-axis and turns around; 
 9 , touches the $x$-axis and turns around; 
 $- 7$, touches the $x$-axis and turns around 
C)  0 , crosses the $x$-axis;
$- 9$, crosses the $x$-axis;
7 , crosses the $x$-axis 
D)  0 , touches the $x$-axis and turns around;  
9 , crosses the $x$-axis;
$- 7$, crosses the $x$-axis 
A)  0 , touches the $x$-axis and turns around;
$- 9$, crosses the $x$-axis;
7 , crosses the $x$-axis 
B)  0 , touches the $x$-axis and turns around; 
 9 , touches the $x$-axis and turns around; 
 $- 7$, touches the $x$-axis and turns around 
C)  0 , crosses the $x$-axis;
$- 9$, crosses the $x$-axis;
7 , crosses the $x$-axis 
D)  0 , touches the $x$-axis and turns around;  
9 , crosses the $x$-axis;
$- 7$, crosses the $x$-axis

Question 16

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

Accepted Answer

A)  $x = - 1 , x = 1 , x = - 3$ 
B)  $x = 1 , x = - 3 , x = 3$ 
C)  $x = - 3 , x = 3$ 
D)  $x = 9$ 
A)  $x = - 1 , x = 1 , x = - 3$ 
B)  $x = 1 , x = - 3 , x = 3$ 
C)  $x = - 3 , x = 3$ 
D)  $x = 9$

Question 17

Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval
notation.
-$$x ^ { 2 } + 7 x \leq - 12$$

Accepted Answer

A)  $[ - 4 , - 3 ]$
  
B)  $( - \infty , 3 ] \cup [ 4 , \infty )$
  
C)  $( 3,4 )$
  
D)  $[ 3,4 ]$
  
A)  $[ - 4 , - 3 ]$
  
B)  $( - \infty , 3 ] \cup [ 4 , \infty )$
  
C)  $( 3,4 )$
  
D)  $[ 3,4 ]$

Question 18

Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval
notation.
-$$\frac { x - 2 } { x + 4 } > 0$$

Accepted Answer

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

Question 19

Find the y-intercept of the polynomial function.
-$$f ( x ) = x \left( 5 - x ^ { 2 } \right)$$

Accepted Answer

A)  origin symmetry 
B)  $y$-axis symmetry 
C)  neither 
A)  origin symmetry 
B)  $y$-axis symmetry 
C)  neither

Question 20

Solve the problem.
-You drive 123 miles along a scenic highway and then take a 25 -mile bike ride. Your driving rate is 4 times your cycling rate. Suppose you have no more than a total of 7 hours for driving and cycling. Let $x$ represent your cycling rate in miles per hour. Write a rational inequality that can be used to determine the possible values of x. Do not simplify and do not solve the inequality.

Accepted Answer

A)  $\frac { 123 } { 4 x } + \frac { 25 } { x } \leq 7$ 
B)  $\frac { 123 } { x } + \frac { 25 } { 4 x } \leq 7$ 
C)  $\frac { 4 x } { 123 } + \frac { x } { 25 } \leq 7$ 
D)  $\frac { 123 } { 4 x } + \frac { 25 } { x } \geq 7$ 
A)  $\frac { 123 } { 4 x } + \frac { 25 } { x } \leq 7$ 
B)  $\frac { 123 } { x } + \frac { 25 } { 4 x } \leq 7$ 
C)  $\frac { 4 x } { 123 } + \frac { x } { 25 } \leq 7$ 
D)  $\frac { 123 } { 4 x } + \frac { 25 } { x } \geq 7$

Find the y-intercept of the polynomial function. -

Graph the polynomial function. - $f(x)=4 x^{2}-x^{3}$ $Graph the polynomial function. - f(x)=4 x^{2}-x^{3}$

Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for the given function. - $f ( x ) = x ^ { 5 } - 3.2 x ^ { 4 } - 19.58 x ^ { 3 } + 3 x ^ { 2 } + 49.21 x - 13.538$

Use synthetic division to show that the number given to the right of the equation is a solution of the equation, then solve the polynomial equation. - $3 x ^ { 3 } + 8 x ^ { 2 } - 13 x - 30 = 0 ; - 3$

Graph the polynomial function. - $f(x)=\frac{1}{4}-\frac{1}{4} x^{4}$ $Graph the polynomial function. - f(x)=\frac{1}{4}-\frac{1}{4} x^{4}$

Divide using long division. -The width of a rectangle is $x - \frac { 1 } { 3 }$ feet and its area is $3 x ^ { 3 } + 17 x ^ { 2 } + 21 x - 9$ square feet. Write a polynomial that represents the length of the rectangle.

Graph the polynomial function. - $f ( x ) = - 2 x ^ { 3 } ( x - 2 ) ^ { 2 } ( x - 1 )$ $Graph the polynomial function. - f ( x ) = - 2 x ^ { 3 } ( x - 2 ) ^ { 2 } ( x - 1 )$

Find the domain of the rational function. - $h ( x ) = \frac { x + 4 } { x ^ { 2 } - 64 }$

Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for the given function. - $f ( x ) = 9 x ^ { 3 } - 7 x ^ { 2 } + x + 4.5$

Graph the polynomial function. - $f(x)=(x-3)(x-2)(x+1)^{2}$ $Graph the polynomial function. - f(x)=(x-3)(x-2)(x+1)^{2}$

Graph the rational function. - $f(x)=\frac{4}{x^{2}+10 x+25}$ $Graph the rational function. - f(x)=\frac{4}{x^{2}+10 x+25}$

Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots. - $x ^ { 4 } + 5 x ^ { 3 } - 2 x ^ { 2 } - 18 x - 12 = 0$

Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for the given function. - $f ( x ) = - 7 x ^ { 9 } + x ^ { 7 } - x ^ { 2 } + 3$

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end - $f ( x ) = - 3 x ^ { 4 } + 2 x ^ { 3 } + 5 x ^ { 2 } - 5 x - 2$

Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. - $x ^ { 4 } + 2 x ^ { 3 } - 63 x ^ { 2 } = 0$

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

Find the y-intercept of the polynomial function. - $f ( x ) = x \left( 5 - x ^ { 2 } \right)$

Equations and Inequalities

Functions and Graphs

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections and Analytic Geometry

Sequences, Induction, and Probability

Prerequisites: Fundamental Concepts of Algebra

Filters

Exam 3: Polynomial and Rational Functions

Find the y-intercept of the polynomial function. -

Graph the polynomial function. - f(x)=4x2−x3f(x)=4 x^{2}-x^{3}f(x)=4x2−x3

Use synthetic division to show that the number given to the right of the equation is a solution of the equation, then solve the polynomial equation. - 3x3+8x2−13x−30=0;−33 x ^ { 3 } + 8 x ^ { 2 } - 13 x - 30 = 0 ; - 33x3+8x2−13x−30=0;−3

Graph the polynomial function. - f(x)=14−14x4f(x)=\frac{1}{4}-\frac{1}{4} x^{4}f(x)=41​−41​x4

Divide using long division. -The width of a rectangle is x−13x - \frac { 1 } { 3 }x−31​ feet and its area is 3x3+17x2+21x−93 x ^ { 3 } + 17 x ^ { 2 } + 21 x - 93x3+17x2+21x−9 square feet. Write a polynomial that represents the length of the rectangle.

Graph the polynomial function. - f(x)=−2x3(x−2)2(x−1)f ( x ) = - 2 x ^ { 3 } ( x - 2 ) ^ { 2 } ( x - 1 )f(x)=−2x3(x−2)2(x−1)

Find the domain of the rational function. - h(x)=x+4x2−64h ( x ) = \frac { x + 4 } { x ^ { 2 } - 64 }h(x)=x2−64x+4​

Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for the given function. - f(x)=9x3−7x2+x+4.5f ( x ) = 9 x ^ { 3 } - 7 x ^ { 2 } + x + 4.5f(x)=9x3−7x2+x+4.5

Graph the polynomial function. - f(x)=(x−3)(x−2)(x+1)2f(x)=(x-3)(x-2)(x+1)^{2}f(x)=(x−3)(x−2)(x+1)2

Graph the rational function. - f(x)=4x2+10x+25f(x)=\frac{4}{x^{2}+10 x+25}f(x)=x2+10x+254​

Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots. - x4+5x3−2x2−18x−12=0x ^ { 4 } + 5 x ^ { 3 } - 2 x ^ { 2 } - 18 x - 12 = 0x4+5x3−2x2−18x−12=0

Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for the given function. - f(x)=−7x9+x7−x2+3f ( x ) = - 7 x ^ { 9 } + x ^ { 7 } - x ^ { 2 } + 3f(x)=−7x9+x7−x2+3

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end - f(x)=−3x4+2x3+5x2−5x−2f ( x ) = - 3 x ^ { 4 } + 2 x ^ { 3 } + 5 x ^ { 2 } - 5 x - 2f(x)=−3x4+2x3+5x2−5x−2

Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. - x4+2x3−63x2=0x ^ { 4 } + 2 x ^ { 3 } - 63 x ^ { 2 } = 0x4+2x3−63x2=0

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

Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. - x2+7x≤−12x ^ { 2 } + 7 x \leq - 12x2+7x≤−12

Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation. - x−2x+4>0\frac { x - 2 } { x + 4 } > 0x+4x−2​>0

Find the y-intercept of the polynomial function. - f(x)=x(5−x2)f ( x ) = x \left( 5 - x ^ { 2 } \right)f(x)=x(5−x2)

Equations and Inequalities

Functions and Graphs

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections and Analytic Geometry

Sequences, Induction, and Probability

Prerequisites: Fundamental Concepts of Algebra

Filters

Graph the polynomial function. - $f(x)=4 x^{2}-x^{3}$ $Graph the polynomial function. - f(x)=4 x^{2}-x^{3}$

Use synthetic division to show that the number given to the right of the equation is a solution of the equation, then solve the polynomial equation. - $3 x ^ { 3 } + 8 x ^ { 2 } - 13 x - 30 = 0 ; - 3$

Graph the polynomial function. - $f(x)=\frac{1}{4}-\frac{1}{4} x^{4}$ $Graph the polynomial function. - f(x)=\frac{1}{4}-\frac{1}{4} x^{4}$

Divide using long division. -The width of a rectangle is $x - \frac { 1 } { 3 }$ feet and its area is $3 x ^ { 3 } + 17 x ^ { 2 } + 21 x - 9$ square feet. Write a polynomial that represents the length of the rectangle.

Graph the polynomial function. - $f ( x ) = - 2 x ^ { 3 } ( x - 2 ) ^ { 2 } ( x - 1 )$ $Graph the polynomial function. - f ( x ) = - 2 x ^ { 3 } ( x - 2 ) ^ { 2 } ( x - 1 )$

Find the domain of the rational function. - $h ( x ) = \frac { x + 4 } { x ^ { 2 } - 64 }$

Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for the given function. - $f ( x ) = 9 x ^ { 3 } - 7 x ^ { 2 } + x + 4.5$

Graph the polynomial function. - $f(x)=(x-3)(x-2)(x+1)^{2}$ $Graph the polynomial function. - f(x)=(x-3)(x-2)(x+1)^{2}$

Graph the rational function. - $f(x)=\frac{4}{x^{2}+10 x+25}$ $Graph the rational function. - f(x)=\frac{4}{x^{2}+10 x+25}$

Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots. - $x ^ { 4 } + 5 x ^ { 3 } - 2 x ^ { 2 } - 18 x - 12 = 0$

Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for the given function. - $f ( x ) = - 7 x ^ { 9 } + x ^ { 7 } - x ^ { 2 } + 3$

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end - $f ( x ) = - 3 x ^ { 4 } + 2 x ^ { 3 } + 5 x ^ { 2 } - 5 x - 2$

Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. - $x ^ { 4 } + 2 x ^ { 3 } - 63 x ^ { 2 } = 0$

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

Find the y-intercept of the polynomial function. - $f ( x ) = x \left( 5 - x ^ { 2 } \right)$