Question 1

Determine the maximum possible number of turning points for the graph of the function.
-$$f ( x ) = ( x - 4 ) ( x + 1 ) ( x + 7 ) ( x - 3 )$$

Accepted Answer

A)  3 
B)  4 
C)  0 
D)  1 Solve. 
A)  3 
B)  4 
C)  0 
D)  1 Solve.

Question 2

Solve the problem.
-The rational function
$$C ( x ) = \frac { 135 x } { 100 - x } , 0 \leq x < 100$$
describes the cost, $\mathrm { C }$, in millions of dollars, to inoculate $x \%$ of the population against a particular strain of the flu. Determine the difference in cost between inoculating $65 \%$ of the population and inoculating $40 \%$ of the population. (Round to the nearest tenth, if necessary.)

Accepted Answer

A)  $\$ 160.7$ million 
B)  $\$ 1.3$ million 
C)  $\$ 160.8$ million 
D)  $\$ 1.4$ million 
A)  $\$ 160.7$ million 
B)  $\$ 1.3$ million 
C)  $\$ 160.8$ million 
D)  $\$ 1.4$ million

Question 3

Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval
notation.
-$$x ^ { 2 } - 2 x \geq 8$$

Accepted Answer

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

Question 4

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.
-$$x ^ { 5 } - 27 x ^ { 3 } + 50 x = 0$$

Accepted Answer

A)  0 , crosses the $x$-axis;
5 , crosses the $x$-axis;
$- 5$, crosses the $x$-axis;
$\sqrt { 2 }$, crosses the $x$-axis;
$- \sqrt { 2 }$, crosses the $x$-axis 
B)  0 , touches the $x$-axis and turns around;
5 , crosses the $x$-axis;
$- 5$, crosses the $x$-axis;
$\sqrt { 2 }$, crosses the $x$-axis;
$- \sqrt { 2 }$, crosses the $x$-axis 
C)  0 , crosses the $x$-axis;
25 , touches the $x$-axis and turns around;
2 , touches the $x$-axis and turns around 
D)  0 , touches the $x$-axis and turns around;
25 , touches the $x$-axis and turns around;
2 , touches the $x$-axis and turns around 
A)  0 , crosses the $x$-axis;
5 , crosses the $x$-axis;
$- 5$, crosses the $x$-axis;
$\sqrt { 2 }$, crosses the $x$-axis;
$- \sqrt { 2 }$, crosses the $x$-axis 
B)  0 , touches the $x$-axis and turns around;
5 , crosses the $x$-axis;
$- 5$, crosses the $x$-axis;
$\sqrt { 2 }$, crosses the $x$-axis;
$- \sqrt { 2 }$, crosses the $x$-axis 
C)  0 , crosses the $x$-axis;
25 , touches the $x$-axis and turns around;
2 , touches the $x$-axis and turns around 
D)  0 , touches the $x$-axis and turns around;
25 , touches the $x$-axis and turns around;
2 , touches the $x$-axis and turns around

Question 5

Find the y-intercept for the graph of the quadratic function.
-$$f ( x ) = x ^ { 2 } + 5 x - 4$$

Accepted Answer

A)  $( 0 , - 4 )$ 
B)  $( 0,1 )$ 
C)  $( 0,4 )$ 
D)  $( 0,5 )$ 
A)  $( 0 , - 4 )$ 
B)  $( 0,1 )$ 
C)  $( 0,4 )$ 
D)  $( 0,5 )$

Question 6

Determine the constant of variation for the stated condition.
-$c$ varies jointly as a and $b$, and $c = 2475$ when $a = 45$ and $b = 11$.

Accepted Answer

A)  $\mathrm { k } = 5$ 
B)  $\mathrm { k } = \frac { 1 } { 9 }$ 
C)  $\mathrm { k } = \frac { 1 } { 5 }$ 
D)  $\mathrm { k } = 9$ 
A)  $\mathrm { k } = 5$ 
B)  $\mathrm { k } = \frac { 1 } { 9 }$ 
C)  $\mathrm { k } = \frac { 1 } { 5 }$ 
D)  $\mathrm { k } = 9$

Question 7

Divide using long division.
-$$\frac { 8 z ^ { 4 } + 12 z ^ { 3 } - 2 z } { 2 z ^ { 2 } + z }$$

Accepted Answer

A)  $4 z ^ { 2 } + 4 z - 2$ 
B)  $4 z ^ { 2 } + 8 z + 4 + \frac { 2 z } { 2 z ^ { 2 } + z }$ 
C)  $4 z ^ { 2 } + 4 z - \frac { 6 z } { 2 z ^ { 2 } + z }$ 
D)  $4 z ^ { 2 } + 6 z - \frac { 2 z } { 2 z ^ { 2 } + z }$ 
A)  $4 z ^ { 2 } + 4 z - 2$ 
B)  $4 z ^ { 2 } + 8 z + 4 + \frac { 2 z } { 2 z ^ { 2 } + z }$ 
C)  $4 z ^ { 2 } + 4 z - \frac { 6 z } { 2 z ^ { 2 } + z }$ 
D)  $4 z ^ { 2 } + 6 z - \frac { 2 z } { 2 z ^ { 2 } + z }$

Question 8

Find the indicated intercept(s) of the graph of the function.
-$y$-intercept of $f ( x ) = \frac { x - 8 } { x ^ { 2 } + 2 x - 8 }$

Accepted Answer

A)  $( 0,1 )$ 
B)  $( 0,8 )$ 
C)  $( 0 , - 1 )$ 
D)  none 
A)  $( 0,1 )$ 
B)  $( 0,8 )$ 
C)  $( 0 , - 1 )$ 
D)  none

Question 9

Find a rational zero of the polynomial function and use it to find all the zeros of the function.
-$$f ( x ) = 2 x ^ { 4 } - 15 x ^ { 3 } + 45 x ^ { 2 } - 45 x + 13$$

Accepted Answer

A)  $\left\{ 1 , \frac { 1 } { 2 } , 3 + 2 i , 3 - 2 i \right\}$ 
B)  $\left\{ - 1 , - \frac { 1 } { 2 } , 2 + 3 i , 2 - 3 i \right\}$ 
C)  $\left\{ 1 , - \frac { 1 } { 2 } , 2 + 3 i , 2 - 3 i \right\}$ 
D)  $\left\{ - 1 , \frac { 1 } { 2 } , 3 + 2 i , 3 - 2 i \right\}$ 
A)  $\left\{ 1 , \frac { 1 } { 2 } , 3 + 2 i , 3 - 2 i \right\}$ 
B)  $\left\{ - 1 , - \frac { 1 } { 2 } , 2 + 3 i , 2 - 3 i \right\}$ 
C)  $\left\{ 1 , - \frac { 1 } { 2 } , 2 + 3 i , 2 - 3 i \right\}$ 
D)  $\left\{ - 1 , \frac { 1 } { 2 } , 3 + 2 i , 3 - 2 i \right\}$

Question 10

Use the Rational Zero Theorem to list all possible rational zeros for the given function.
-$$f ( x ) = - 4 x ^ { 4 } + 3 x ^ { 2 } - 2 x + 6$$

Accepted Answer

A)  $\pm \frac { 1 } { 4 } , \pm \frac { 1 } { 2 } , \pm \frac { 3 } { 4 } , \pm \frac { 3 } { 2 } , \pm 1 , \pm 2 , \pm 3 , \pm 6$ 
B)  $\pm \frac { 1 } { 6 } , \pm \frac { 1 } { 2 } , \pm \frac { 1 } { 3 } , \pm \frac { 2 } { 3 } , \pm \frac { 4 } { 3 } , \pm 1 , \pm 2 , \pm 4$ 
C)  $\pm \frac { 1 } { 4 } , \pm \frac { 1 } { 2 } , \pm \frac { 3 } { 4 } , \pm \frac { 3 } { 2 } , \pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 6$ 
D)  $\pm \frac { 1 } { 4 } , \pm \frac { 1 } { 2 } , \pm \frac { 2 } { 3 } , \pm \frac { 3 } { 4 } , \pm \frac { 3 } { 2 } , \pm 1 , \pm 2 , \pm 3 , \pm 6$ 
A)  $\pm \frac { 1 } { 4 } , \pm \frac { 1 } { 2 } , \pm \frac { 3 } { 4 } , \pm \frac { 3 } { 2 } , \pm 1 , \pm 2 , \pm 3 , \pm 6$ 
B)  $\pm \frac { 1 } { 6 } , \pm \frac { 1 } { 2 } , \pm \frac { 1 } { 3 } , \pm \frac { 2 } { 3 } , \pm \frac { 4 } { 3 } , \pm 1 , \pm 2 , \pm 4$ 
C)  $\pm \frac { 1 } { 4 } , \pm \frac { 1 } { 2 } , \pm \frac { 3 } { 4 } , \pm \frac { 3 } { 2 } , \pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 6$ 
D)  $\pm \frac { 1 } { 4 } , \pm \frac { 1 } { 2 } , \pm \frac { 2 } { 3 } , \pm \frac { 3 } { 4 } , \pm \frac { 3 } { 2 } , \pm 1 , \pm 2 , \pm 3 , \pm 6$

Question 11

Graph the function.
-$f(x)=\frac{x^{2}+2 x-7}{x-5}$

Accepted Answer

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

Question 12

Find the y-intercept of the polynomial function.
-$$f ( x ) = 4 x ^ { 2 } - x ^ { 3 }$$

Accepted Answer

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

Question 13

Find the y-intercept for the graph of the quadratic function.
-$$f ( x ) = 2 + 3 x + x ^ { 2 }$$

Accepted Answer

A)  $( 0,2 )$ 
B)  $( 0,1 )$ 
C)  $( 0 , - 2 )$ 
D)  $( 0,3 )$ 
A)  $( 0,2 )$ 
B)  $( 0,1 )$ 
C)  $( 0 , - 2 )$ 
D)  $( 0,3 )$

Question 14

Find a rational zero of the polynomial function and use it to find all the zeros of the function.
-$$f ( x ) = x ^ { 4 } - 4 x ^ { 3 } + 22 x ^ { 2 } - 36 x - 208$$

Accepted Answer

A)  $\{ - 2,4,1 + 5 i , 1 - 5 i \}$ 
B)  $\{ 2 , - 4,1 + 5 i , 1 - 5 i \}$ 
C)  $\{ - 2,4,1 + 6 i , 1 - 6 i \}$ 
D)  $\{ 2 , - 4,1 + \sqrt { 5 } , 1 - \sqrt { 5 } \}$ 
A)  $\{ - 2,4,1 + 5 i , 1 - 5 i \}$ 
B)  $\{ 2 , - 4,1 + 5 i , 1 - 5 i \}$ 
C)  $\{ - 2,4,1 + 6 i , 1 - 6 i \}$ 
D)  $\{ 2 , - 4,1 + \sqrt { 5 } , 1 - \sqrt { 5 } \}$

Question 15

Determine the constant of variation for the stated condition.
-If the resistance in an electrical circuit is held constant, the amount of current flowing through the circuit is directly proportional to the amount of voltage applied to the circuit. When 4 volts are applied to a circuit, 100 milliamperes of current flow through the circuit. Find the new current if the voltage is increased to 13 volts.

Accepted Answer

A)  325 milliamperes 
B)  52 milliamperes 
C)  312 milliamperes 
D)  350 milliamperes 
A)  325 milliamperes 
B)  52 milliamperes 
C)  312 milliamperes 
D)  350 milliamperes

Question 16

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses
the x-axis or touches the x-axis and turns around, at each zero.
-$$f ( x ) = x ^ { 3 } + x ^ { 2 } - 42 x$$

Accepted Answer

A)  0 , multiplicity 1 , crosses the $x$-axis
$- 7$, multiplicity 1 , crosses the $x$-axis
6 , multiplicity 1 , crosses the $x$-axis 
B)  $- 7$, multiplicity 2 , touches the $x$-axis and turns around 
6, multiplicity 1 , crosses the $x$-axis 
C)  0 , multiplicity 1 , crosses the $x$-axis
7 , multiplicity 1 , crosses the $x$-axis 
$- 6$, multiplicity 1 , crosses the $x$-axis 
D)  0 , multiplicity 1 , touches the $x$-axis and turns around;
 $- 7$, multiplicity 1 , touches the $x$-axis and turns around; 
6 , multiplicity 1 , touches the $x$-axis and turns around 
A)  0 , multiplicity 1 , crosses the $x$-axis
$- 7$, multiplicity 1 , crosses the $x$-axis
6 , multiplicity 1 , crosses the $x$-axis 
B)  $- 7$, multiplicity 2 , touches the $x$-axis and turns around 
6, multiplicity 1 , crosses the $x$-axis 
C)  0 , multiplicity 1 , crosses the $x$-axis
7 , multiplicity 1 , crosses the $x$-axis 
$- 6$, multiplicity 1 , crosses the $x$-axis 
D)  0 , multiplicity 1 , touches the $x$-axis and turns around;
 $- 7$, multiplicity 1 , touches the $x$-axis and turns around; 
6 , multiplicity 1 , touches the $x$-axis and turns around

Question 17

Determine the constant of variation for the stated condition.
-$y = 4$ when $x = 6$

Accepted Answer

A)  $y = \frac { 2 } { 3 } x$ 
B)  $y = \frac { 3 } { 2 } x$ 
C)  $y = x - 2$ 
D)  $y = 2 x$ y 
A)  $y = \frac { 2 } { 3 } x$ 
B)  $y = \frac { 3 } { 2 } x$ 
C)  $y = x - 2$ 
D)  $y = 2 x$ y

Question 18

Solve the problem.
-Among all pairs of numbers whose difference is 48, find a pair whose product is as small as possible.

Accepted Answer

A)  -24 and 24 
B)  24 and 24 
C)  -72 and -24 
D)  72 and 24 
A)  -24 and 24 
B)  24 and 24 
C)  -72 and -24 
D)  72 and 24

Question 19

Graph the polynomial function.
-$f(x)=x^{3}+2 x^{2}-5 x-6$

Accepted Answer

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

Question 20

Determine the constant of variation for the stated condition.
-$\mathrm { f }$ varies jointly as $\mathrm { q } ^ { 2 }$ and $h$, and $\mathrm { f } = 96$ when $\mathrm { q } = 4$ and $\mathrm { h } = 2$. Find $h$ when $\mathrm { f } = 135$ and $\mathrm { q } = 3$.

Accepted Answer

A)  $h = 5$ 
B)  $h = 2$ 
C)  $h = 4$ 
D)  $h = 3$ 
A)  $h = 5$ 
B)  $h = 2$ 
C)  $h = 4$ 
D)  $h = 3$

Determine the maximum possible number of turning points for the graph of the function. - $f ( x ) = ( x - 4 ) ( x + 1 ) ( x + 7 ) ( x - 3 )$

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. - $x ^ { 5 } - 27 x ^ { 3 } + 50 x = 0$

Find the y-intercept for the graph of the quadratic function. - $f ( x ) = x ^ { 2 } + 5 x - 4$

Determine the constant of variation for the stated condition. - $c$ varies jointly as a and $b$ , and $c = 2475$ when $a = 45$ and $b = 11$ .

Divide using long division. - $\frac { 8 z ^ { 4 } + 12 z ^ { 3 } - 2 z } { 2 z ^ { 2 } + z }$

Find the indicated intercept(s) of the graph of the function. - $y$ -intercept of $f ( x ) = \frac { x - 8 } { x ^ { 2 } + 2 x - 8 }$

Find a rational zero of the polynomial function and use it to find all the zeros of the function. - $f ( x ) = 2 x ^ { 4 } - 15 x ^ { 3 } + 45 x ^ { 2 } - 45 x + 13$

Use the Rational Zero Theorem to list all possible rational zeros for the given function. - $f ( x ) = - 4 x ^ { 4 } + 3 x ^ { 2 } - 2 x + 6$

Graph the function. - $f(x)=\frac{x^{2}+2 x-7}{x-5}$ $Graph the function. - f(x)=\frac{x^{2}+2 x-7}{x-5}$

Find the y-intercept of the polynomial function. - $f ( x ) = 4 x ^ { 2 } - x ^ { 3 }$

Find the y-intercept for the graph of the quadratic function. - $f ( x ) = 2 + 3 x + x ^ { 2 }$

Find a rational zero of the polynomial function and use it to find all the zeros of the function. - $f ( x ) = x ^ { 4 } - 4 x ^ { 3 } + 22 x ^ { 2 } - 36 x - 208$

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. - $f ( x ) = x ^ { 3 } + x ^ { 2 } - 42 x$

Determine the constant of variation for the stated condition. - $y = 4$ when $x = 6$

Solve the problem. -Among all pairs of numbers whose difference is 48, find a pair whose product is as small as possible.

Graph the polynomial function. - $f(x)=x^{3}+2 x^{2}-5 x-6$ $Graph the polynomial function. - f(x)=x^{3}+2 x^{2}-5 x-6$

Determine the constant of variation for the stated condition. - $\mathrm { f }$ varies jointly as $\mathrm { q } ^ { 2 }$ and $h$ , and $\mathrm { f } = 96$ when $\mathrm { q } = 4$ and $\mathrm { h } = 2$ . Find $h$ when $\mathrm { f } = 135$ and $\mathrm { q } = 3$ .

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

Determine the maximum possible number of turning points for the graph of the function. - f(x)=(x−4)(x+1)(x+7)(x−3)f ( x ) = ( x - 4 ) ( x + 1 ) ( x + 7 ) ( x - 3 )f(x)=(x−4)(x+1)(x+7)(x−3)

Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. - x2−2x≥8x ^ { 2 } - 2 x \geq 8x2−2x≥8

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. - x5−27x3+50x=0x ^ { 5 } - 27 x ^ { 3 } + 50 x = 0x5−27x3+50x=0

Find the y-intercept for the graph of the quadratic function. - f(x)=x2+5x−4f ( x ) = x ^ { 2 } + 5 x - 4f(x)=x2+5x−4

Determine the constant of variation for the stated condition. - ccc varies jointly as a and bbb , and c=2475c = 2475c=2475 when a=45a = 45a=45 and b=11b = 11b=11 .

Divide using long division. - 8z4+12z3−2z2z2+z\frac { 8 z ^ { 4 } + 12 z ^ { 3 } - 2 z } { 2 z ^ { 2 } + z }2z2+z8z4+12z3−2z​

Find the indicated intercept(s) of the graph of the function. - yyy -intercept of f(x)=x−8x2+2x−8f ( x ) = \frac { x - 8 } { x ^ { 2 } + 2 x - 8 }f(x)=x2+2x−8x−8​

Find a rational zero of the polynomial function and use it to find all the zeros of the function. - f(x)=2x4−15x3+45x2−45x+13f ( x ) = 2 x ^ { 4 } - 15 x ^ { 3 } + 45 x ^ { 2 } - 45 x + 13f(x)=2x4−15x3+45x2−45x+13

Use the Rational Zero Theorem to list all possible rational zeros for the given function. - f(x)=−4x4+3x2−2x+6f ( x ) = - 4 x ^ { 4 } + 3 x ^ { 2 } - 2 x + 6f(x)=−4x4+3x2−2x+6

Graph the function. - f(x)=x2+2x−7x−5f(x)=\frac{x^{2}+2 x-7}{x-5}f(x)=x−5x2+2x−7​

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

Find the y-intercept for the graph of the quadratic function. - f(x)=2+3x+x2f ( x ) = 2 + 3 x + x ^ { 2 }f(x)=2+3x+x2

Find a rational zero of the polynomial function and use it to find all the zeros of the function. - f(x)=x4−4x3+22x2−36x−208f ( x ) = x ^ { 4 } - 4 x ^ { 3 } + 22 x ^ { 2 } - 36 x - 208f(x)=x4−4x3+22x2−36x−208

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. - f(x)=x3+x2−42xf ( x ) = x ^ { 3 } + x ^ { 2 } - 42 xf(x)=x3+x2−42x

Determine the constant of variation for the stated condition. - y=4y = 4y=4 when x=6x = 6x=6