Question 1

Find a rational zero of the polynomial function and use it to find all the zeros of the function.
-$$f ( x ) = x ^ { 3 } - 8 x ^ { 2 } - x + 8$$

Accepted Answer

A)  $\{ 1 , - 1,8 \}$ 
B)  $\{ - 1,2 , - 4 \}$ 
C)  $\{ 1,2,4 \}$ 
D)  $\{ 1 , - 1 , - 8 \}$ 
A)  $\{ 1 , - 1,8 \}$ 
B)  $\{ - 1,2 , - 4 \}$ 
C)  $\{ 1,2,4 \}$ 
D)  $\{ 1 , - 1 , - 8 \}$

Question 2

Determine the maximum possible number of turning points for the graph of the function.
-$$f ( x ) = x ^ { 5 } \left( x ^ { 5 } - 4 \right) ( 4 x + 5 )$$

Accepted Answer

A)  10 
B)  11 
C)  40 
D)  5 
A)  10 
B)  11 
C)  40 
D)  5

Question 3

Use the Rational Zero Theorem to list all possible rational zeros for the given function.
-$$f ( x ) = 3 x ^ { 5 } - 5 x ^ { 2 } + 3 x - 1$$

Accepted Answer

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

Question 4

Find a rational zero of the polynomial function and use it to find all the zeros of the function.
-$$f ( x ) = 2 x ^ { 4 } + 17 x ^ { 3 } + 58 x ^ { 2 } + 77 x + 26$$

Accepted Answer

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

Question 5

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.
-Crosses the $x$-axis at $- 3,0$, and 1 ; lies above the $x$-axis between $- 3$ and 0 ; lies below the $x$-axis between 0 and $1 .$

Accepted Answer

A)  $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 3 x$ 
B)  $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 3 x$ 
C)  $f ( x ) = - x ^ { 3 } - 2 x ^ { 2 } + 3 x$ 
D)  $f ( x ) = - x ^ { 3 } + 2 x ^ { 2 } + 3 x$ 
A)  $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 3 x$ 
B)  $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 3 x$ 
C)  $f ( x ) = - x ^ { 3 } - 2 x ^ { 2 } + 3 x$ 
D)  $f ( x ) = - x ^ { 3 } + 2 x ^ { 2 } + 3 x$

Question 6

Write an equation that expresses the relationship. Use k as the constant of variation.
-$x$ varies inversely as $y ^ { 2 }$, and $x = 3$ when $y = 12$. Find $x$ when $y = 2$.

Accepted Answer

A)  $x = 108$ 
B)  $x = 54$ 
C)  $x = 12$ 
D)  $x = 6$ Solve. 
A)  $x = 108$ 
B)  $x = 54$ 
C)  $x = 12$ 
D)  $x = 6$ Solve.

Question 7

Solve Problems Involving Joint Variation
-f varies jointly as s and c.

Accepted Answer

A)  $\mathrm { f } = \mathrm { ksc }$ 
B)  $f = \frac { k s } { c }$ 
C)  $f = k s k c$ 
D)  $f = \frac { k c } { s }$ 
A)  $\mathrm { f } = \mathrm { ksc }$ 
B)  $f = \frac { k s } { c }$ 
C)  $f = k s k c$ 
D)  $f = \frac { k c } { s }$

Question 8

Find the axis of symmetry of the parabola defined by the given quadratic function.
-$$f ( x ) = 5 x ^ { 2 } + 10 x - 6$$

Accepted Answer

A)  $x = - 1$ 
B)  $x = 1$ 
C)  $x = - 2$ 
D)  $x = - 11$ 
A)  $x = - 1$ 
B)  $x = 1$ 
C)  $x = - 2$ 
D)  $x = - 11$

Question 9

Find a rational zero of the polynomial function and use it to find all the zeros of the function.
-$$f ( x ) = 2 x ^ { 3 } - x ^ { 2 } - 6 x + 3$$

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

Determine the constant of variation for the stated condition.
-The amount of simple interest earned on an investment over a fixed amount of time is jointly proportional to the principle invested and the interest rate. A principle investment of $2000.00 with an interest rate of 1% earned $100.00 in simple interest. Find the amount of simple interest earned if the principle is $3500.00 and the interest rate is 8%.

Accepted Answer

A)  $1400.00 
B)  $140,000.00 
C)  $175.00 
D)  $800.00 
A)  $1400.00 
B)  $140,000.00 
C)  $175.00 
D)  $800.00

Question 12

Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval
notation.
-$$\frac { x - 3 } { x + 9 } < 0$$

Accepted Answer

A)  $( - 9,3 )$
  
B)  $( - \infty , - 9 )$ or $( 3 , \infty )$
  
C)  $( 3 , \infty )$
  
D)  $( - \infty , - 9 )$
  
A)  $( - 9,3 )$
  
B)  $( - \infty , - 9 )$ or $( 3 , \infty )$
  
C)  $( 3 , \infty )$
  
D)  $( - \infty , - 9 )$

Question 13

Find the horizontal asymptote, if any, of the graph of the rational function.
-$$f ( x ) = \frac { - 25 x } { 5 x ^ { 3 } + x ^ { 2 } + 1 }$$

Accepted Answer

A)  $y = 0$ 
B)  $y = - 5$ 
C)  $y = - \frac { 1 } { 5 }$ 
D)  no horizontal asymptote 
A)  $y = 0$ 
B)  $y = - 5$ 
C)  $y = - \frac { 1 } { 5 }$ 
D)  no horizontal asymptote

Question 14

Determine the constant of variation for the stated condition.
-$c$ varies jointly as $a$ and $b$. Find $c$ when $a = 15 , b = 13$, and $k = 3$.

Accepted Answer

A)  $\mathrm { c } = 585$ 
B)  $\mathrm { c } = 195$ 
C)  $\mathrm { c } = 65$ 
D)  $\mathrm { c } = \frac { 13 } { 5 }$ 
A)  $\mathrm { c } = 585$ 
B)  $\mathrm { c } = 195$ 
C)  $\mathrm { c } = 65$ 
D)  $\mathrm { c } = \frac { 13 } { 5 }$

Question 15

Determine whether the graph shown is the graph of a polynomial function.
-

Accepted Answer

A)  polynomial function 
B)  not a polynomial function 
A)  polynomial function 
B)  not a polynomial function

Question 16

Find the axis of symmetry of the parabola defined by the given quadratic function.
-$$f ( x ) = - x ^ { 2 } + 14 x + 4$$

Accepted Answer

A)  $x = 7$ 
B)  $x = - 7$ 
C)  $x = 14$ 
D)  $x = 53$ 
A)  $x = 7$ 
B)  $x = - 7$ 
C)  $x = 14$ 
D)  $x = 53$

Question 17

Write an equation that expresses the relationship. Use k as the constant of variation.
-$$\mathrm { y } = 0.2 \text { when } \mathrm { x } = 0.5$$

Accepted Answer

A)  $\mathrm { y } = \frac { 0.1 } { \mathrm { x } }$ 
B)  $y = 0.4 x$ 
C)  $y = 10 x$ 
D)  $\mathrm { y } = \frac { 10 } { \mathrm { x } }$ 
A)  $\mathrm { y } = \frac { 0.1 } { \mathrm { x } }$ 
B)  $y = 0.4 x$ 
C)  $y = 10 x$ 
D)  $\mathrm { y } = \frac { 10 } { \mathrm { x } }$

Question 18

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

Accepted Answer

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

Question 19

Find the indicated intercept(s) of the graph of the function.
-$x$-intercepts of $f ( x ) = \frac { x - 4 } { x ^ { 2 } + 5 x - 2 }$

Accepted Answer

A)  $( 4,0 )$ 
B)  $( 2,0 )$ 
C)  $( 5,0 )$ 
D)  none 
A)  $( 4,0 )$ 
B)  $( 2,0 )$ 
C)  $( 5,0 )$ 
D)  none

Question 20

Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval
notation.
-$$\frac { 15 - 3 x } { 5 x + 3 } \leq 0$$

Accepted Answer

A)  $\left( - \infty , - \frac { 3 } { 5 } \right)$ or $[ 5 , \infty )$
  
B)  $\left[ - \frac { 3 } { 5 } , 5 \right]$
  
C)  $\left[ - \infty , - \frac { 3 } { 5 } \right]$ or $[ 5 , \infty )$
  
D)  $[ 5 , \infty )$
  
A)  $\left( - \infty , - \frac { 3 } { 5 } \right)$ or $[ 5 , \infty )$
  
B)  $\left[ - \frac { 3 } { 5 } , 5 \right]$
  
C)  $\left[ - \infty , - \frac { 3 } { 5 } \right]$ or $[ 5 , \infty )$
  
D)  $[ 5 , \infty )$

Find a rational zero of the polynomial function and use it to find all the zeros of the function. - $f ( x ) = x ^ { 3 } - 8 x ^ { 2 } - x + 8$

Determine the maximum possible number of turning points for the graph of the function. - $f ( x ) = x ^ { 5 } \left( x ^ { 5 } - 4 \right) ( 4 x + 5 )$

Use the Rational Zero Theorem to list all possible rational zeros for the given function. - $f ( x ) = 3 x ^ { 5 } - 5 x ^ { 2 } + 3 x - 1$

Find a rational zero of the polynomial function and use it to find all the zeros of the function. - $f ( x ) = 2 x ^ { 4 } + 17 x ^ { 3 } + 58 x ^ { 2 } + 77 x + 26$

Write an equation that expresses the relationship. Use k as the constant of variation. - $x$ varies inversely as $y ^ { 2 }$ , and $x = 3$ when $y = 12$ . Find $x$ when $y = 2$ .

Solve Problems Involving Joint Variation -f varies jointly as s and c.

Find the axis of symmetry of the parabola defined by the given quadratic function. - $f ( x ) = 5 x ^ { 2 } + 10 x - 6$

Find a rational zero of the polynomial function and use it to find all the zeros of the function. - $f ( x ) = 2 x ^ { 3 } - x ^ { 2 } - 6 x + 3$

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

Find the horizontal asymptote, if any, of the graph of the rational function. - $f ( x ) = \frac { - 25 x } { 5 x ^ { 3 } + x ^ { 2 } + 1 }$

Determine the constant of variation for the stated condition. - $c$ varies jointly as $a$ and $b$ . Find $c$ when $a = 15 , b = 13$ , and $k = 3$ .

Determine whether the graph shown is the graph of a polynomial function. -

Find the axis of symmetry of the parabola defined by the given quadratic function. - $f ( x ) = - x ^ { 2 } + 14 x + 4$

Write an equation that expresses the relationship. Use k as the constant of variation. - $\mathrm { y } = 0.2 \text { when } \mathrm { x } = 0.5$

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

Find the indicated intercept(s) of the graph of the function. - $x$ -intercepts of $f ( x ) = \frac { x - 4 } { x ^ { 2 } + 5 x - 2 }$

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 a rational zero of the polynomial function and use it to find all the zeros of the function. - f(x)=x3−8x2−x+8f ( x ) = x ^ { 3 } - 8 x ^ { 2 } - x + 8f(x)=x3−8x2−x+8

Determine the maximum possible number of turning points for the graph of the function. - f(x)=x5(x5−4)(4x+5)f ( x ) = x ^ { 5 } \left( x ^ { 5 } - 4 \right) ( 4 x + 5 )f(x)=x5(x5−4)(4x+5)

Use the Rational Zero Theorem to list all possible rational zeros for the given function. - f(x)=3x5−5x2+3x−1f ( x ) = 3 x ^ { 5 } - 5 x ^ { 2 } + 3 x - 1f(x)=3x5−5x2+3x−1

Find a rational zero of the polynomial function and use it to find all the zeros of the function. - f(x)=2x4+17x3+58x2+77x+26f ( x ) = 2 x ^ { 4 } + 17 x ^ { 3 } + 58 x ^ { 2 } + 77 x + 26f(x)=2x4+17x3+58x2+77x+26

Write an equation that expresses the relationship. Use k as the constant of variation. - xxx varies inversely as y2y ^ { 2 }y2 , and x=3x = 3x=3 when y=12y = 12y=12 . Find xxx when y=2y = 2y=2 .