Question 1

Find all rational zeros.
-$$f ( x ) = x ^ { 4 } - 7 x ^ { 3 } + 3 x ^ { 2 } + 21 x - 18$$

Accepted Answer

A)  6,1 
B)  $- 6,1$ 
C)  No rational zeros 
D)  $6 , - 1$ 
A)  6,1 
B)  $- 6,1$ 
C)  No rational zeros 
D)  $6 , - 1$

Question 2

Find the remainder when f(x) is divided by (x - k)
-$$f ( x ) = 9 x ^ { 4 } + 8 x ^ { 3 } + 2 x ^ { 2 } - 4 x + 58 ; k = 3$$

Accepted Answer

A)  1569 
B)  1009 
C)  449 
D)  2827 
A)  1569 
B)  1009 
C)  449 
D)  2827

Question 3

Choose the one alternative that best completes the statement or answers the question.
Solve the equation.
-$$\frac { 5 - x } { x } + \frac { 3 } { 4 } = \frac { 7 } { x }$$

Accepted Answer

A)  $x = \frac { \sqrt { 29 } } { 2 \sqrt { 5 } }$ 
B)  $x = 8$ 
C)  $x = - 8$ 
D)  $x = - 4$ 
A)  $x = \frac { \sqrt { 29 } } { 2 \sqrt { 5 } }$ 
B)  $x = 8$ 
C)  $x = - 8$ 
D)  $x = - 4$

Question 4

Match the equation to one of the curves (for x ≥ 0).
-$$f ( x ) = 2.7 x ^ { 2 / 3 }$$

Accepted Answer

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

Question 5

Find the requested function.
-Find the cubic function with the given table of values.

Accepted Answer

A)  $f ( x ) = 2 ( x + 4 ) ( x - 3 ) ( x - 1 )$ 
B)  $f ( x ) = 2 ( x + 4 ) ( x + 3 ) ( x - 1 )$ 
C)  $f ( x ) = ( x + 4 ) ( x + 3 ) ( x - 1 )$ 
D)  $f ( x ) = 2 ( x - 4 ) ( x - 3 ) ( x + 1 )$ 
A)  $f ( x ) = 2 ( x + 4 ) ( x - 3 ) ( x - 1 )$ 
B)  $f ( x ) = 2 ( x + 4 ) ( x + 3 ) ( x - 1 )$ 
C)  $f ( x ) = ( x + 4 ) ( x + 3 ) ( x - 1 )$ 
D)  $f ( x ) = 2 ( x - 4 ) ( x - 3 ) ( x + 1 )$

Question 6

Solve the inequality.
-$$3 + \frac { 14 } { x } - \frac { 5 } { x ^ { 2 } } \leq 0$$

Accepted Answer

A)  $\left[ - 5 , \frac { 1 } { 3 } \right]$ 
B)  $( - \infty , - 5 ] \cup \left[ \frac { 1 } { 3 } , \infty \right)$ 
C)  $[ - 5,0 ) \cup \left( 0 , \frac { 1 } { 3 } \right]$ 
D)  $\left[ \frac { 1 } { 3 } , 5 \right]$ 
A)  $\left[ - 5 , \frac { 1 } { 3 } \right]$ 
B)  $( - \infty , - 5 ] \cup \left[ \frac { 1 } { 3 } , \infty \right)$ 
C)  $[ - 5,0 ) \cup \left( 0 , \frac { 1 } { 3 } \right]$ 
D)  $\left[ \frac { 1 } { 3 } , 5 \right]$

Question 7

Find the vertex of the graph of the function.
-$$f ( x ) = 3 ( x - \sqrt { 5 } ) ^ { 2 } + 5$$

Accepted Answer

A)  $( \sqrt { 5 } , 5 )$ 
B)  $( - 5,5 )$ 
C)  $( 5,5 )$ 
D)  $( - \sqrt { 5 } , 5 )$ 
A)  $( \sqrt { 5 } , 5 )$ 
B)  $( - 5,5 )$ 
C)  $( 5,5 )$ 
D)  $( - \sqrt { 5 } , 5 )$

Question 8

State the power and constant of variation for the function, and then analyze it.
-$$f ( x ) = - 4 x ^ { 1 / 3 }$$

Accepted Answer

Power is 1/3; constant of variation is @#LAT-DLM&;

Question 9

Solve the problem.
-Find the remainder when $x ^ { 49 } - 10$ is divided by $x + 1$.

Accepted Answer

A)  $- 11$ 
B)  9 
C)  $- 9$ 
D)  11 
A)  $- 11$ 
B)  9 
C)  $- 9$ 
D)  11

Question 10

Use a graphing calculator to approximate the real zeros of the function defined by f(x). Express decimal approximations to
the nearest hundredth.
-$$f ( x ) = x ^ { 4 } - 2.44 x ^ { 3 } - 12.25 x ^ { 2 } + 21.56 x + 17.68$$

Accepted Answer

A)  $2.33 , - 0.63 , - 3.12,3.86$ 
B)  $2.33 , - 3.12 , - 3.86$ 
C)  $- 2.33 , - 0.63 , - 3.12 , - 3.86$ 
D)  $0.63 , - 3.86$ 
A)  $2.33 , - 0.63 , - 3.12,3.86$ 
B)  $2.33 , - 3.12 , - 3.86$ 
C)  $- 2.33 , - 0.63 , - 3.12 , - 3.86$ 
D)  $0.63 , - 3.86$

Question 11

List the x- and y-intercepts, and graph the function.
-$$f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } - x - 20 }$$

Accepted Answer

A)  No x-intercepts, $y$-intercept: $( 0 , - 1 )$;
  
B)  $x$-intercept: $( 0,0 ) , y$-intercept: $( 0,0 )$;
  
C)  No $x$-intercepts, no $y$-intercepts ;
  
D)  $x$-intercept: $( 0,0 ) , y$-intercept: $( 0,0 )$;
  
A)  No x-intercepts, $y$-intercept: $( 0 , - 1 )$;
  
B)  $x$-intercept: $( 0,0 ) , y$-intercept: $( 0,0 )$;
  
C)  No $x$-intercepts, no $y$-intercepts ;
  
D)  $x$-intercept: $( 0,0 ) , y$-intercept: $( 0,0 )$;

Question 12

Match the equation to one of the curves (for x ≥ 0).
-$$f ( x ) = \frac { 1 } { 3 } x ^ { - 5 }$$

Accepted Answer

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

Question 13

Describe the end behavior of the polynomial function by finding  
-$$f ( x ) = x ^ { 3 } + x ^ { 4 } - 6 x ^ { 2 } - 7 x + 1$$

Accepted Answer

A)  $-\infty , -\infty$ 
B)  $-\infty , \infty$ 
C)  $\infty , -\infty$ 
D)  $\infty , \infty$ 
A)  $-\infty , -\infty$ 
B)  $-\infty , \infty$ 
C)  $\infty , -\infty$ 
D)  $\infty , \infty$

Question 14

Write an equation for the quadratic function whose graph contains the given vertex and point.
-Vertex $( 3 , - 2 )$, point $( 0,25 )$

Accepted Answer

A)  $P ( x ) = 3 x ^ { 2 } - 18 x + 25$ 
B)  $P ( x ) = 3 x ^ { 2 } - 3 x - 2$ 
C)  $P ( x ) = 0 x ^ { 2 } - 18 x - 25$ 
D)  $P ( x ) = - 3 x ^ { 2 } + 18 x - 2$ 
A)  $P ( x ) = 3 x ^ { 2 } - 18 x + 25$ 
B)  $P ( x ) = 3 x ^ { 2 } - 3 x - 2$ 
C)  $P ( x ) = 0 x ^ { 2 } - 18 x - 25$ 
D)  $P ( x ) = - 3 x ^ { 2 } + 18 x - 2$

Question 15

Match the given graph with its polynomial function.Choose the one alternative that best completes the statement or answers the question.
-

Accepted Answer

A)  $f ( x ) = x ^ { 5 } + 7 x ^ { 4 } - x ^ { 3 } - 40 x ^ { 2 } + 2 x + 16$ 
B)  $f ( x ) = - 2 x ^ { 5 } + 7 x ^ { 4 } + 9 x ^ { 3 } - 40 x ^ { 2 } + 4 x + 16$ 
C)  $f ( x ) = 2 x ^ { 6 } + 9 x ^ { 3 } - 7 x ^ { 2 } + 4 x - 16$ 
D)  $f ( x ) = - x ^ { 6 } + 7 x ^ { 5 } - x ^ { 2 } - 2 x + 16$ 
A)  $f ( x ) = x ^ { 5 } + 7 x ^ { 4 } - x ^ { 3 } - 40 x ^ { 2 } + 2 x + 16$ 
B)  $f ( x ) = - 2 x ^ { 5 } + 7 x ^ { 4 } + 9 x ^ { 3 } - 40 x ^ { 2 } + 4 x + 16$ 
C)  $f ( x ) = 2 x ^ { 6 } + 9 x ^ { 3 } - 7 x ^ { 2 } + 4 x - 16$ 
D)  $f ( x ) = - x ^ { 6 } + 7 x ^ { 5 } - x ^ { 2 } - 2 x + 16$

Question 16

Divide f(x) by d(x), and write a summary statement in the form indicated.
-$f ( x ) = x ^ { 2 } - 2 x + 5 ; d ( x ) = x - 7 \quad$ (Write answer in fraction form)

Accepted Answer

A)  $\frac { f ( x ) } { ( x - 7 ) } = ( x + 5 ) + \frac { 40 } { ( x - 7 ) }$ 
B)  $\frac { f ( x ) } { ( x - 7 ) } = ( x - 7 ) + \frac { 40 } { ( x - 7 ) }$ 
C)  $\frac { f ( x ) } { ( x - 7 ) } = ( x + 5 ) + \frac { 35 } { ( x - 7 ) }$ 
D)  $\frac { f ( x ) } { ( x - 7 ) } = ( x - 7 ) + \frac { 35 } { ( x - 7 ) }$ 
A)  $\frac { f ( x ) } { ( x - 7 ) } = ( x + 5 ) + \frac { 40 } { ( x - 7 ) }$ 
B)  $\frac { f ( x ) } { ( x - 7 ) } = ( x - 7 ) + \frac { 40 } { ( x - 7 ) }$ 
C)  $\frac { f ( x ) } { ( x - 7 ) } = ( x + 5 ) + \frac { 35 } { ( x - 7 ) }$ 
D)  $\frac { f ( x ) } { ( x - 7 ) } = ( x - 7 ) + \frac { 35 } { ( x - 7 ) }$

Question 17

Determine if the function is a power function. If it is, then state the power and constant of variation.
-$$f ( x ) = \frac { 1 } { 3 } x ^ { 2 }$$

Accepted Answer

A)  Power is 2; constant of variation is $\frac { 1 } { 3 }$ 
B)  Power is 2; constant of variation is 2 
C)  Power is $\frac { 1 } { 3 } ;$ constant of variation is 2 
D)  Not a power function 
A)  Power is 2; constant of variation is $\frac { 1 } { 3 }$ 
B)  Power is 2; constant of variation is 2 
C)  Power is $\frac { 1 } { 3 } ;$ constant of variation is 2 
D)  Not a power function

Question 18

Find a cubic function with the given zeros.
-$\sqrt { 2 } , - \sqrt { 2 } , - 7$

Accepted Answer

A)  $f ( x ) = x ^ { 3 } + 7 x ^ { 2 } + 2 x - 14$ 
B)  $f ( x ) = x ^ { 3 } + 7 x ^ { 2 } - 2 x - 14$ 
C)  $f ( x ) = x ^ { 3 } + 7 x ^ { 2 } - 2 x + 14$ 
D)  $f ( x ) = x ^ { 3 } - 7 x ^ { 2 } - 2 x - 14$ 
A)  $f ( x ) = x ^ { 3 } + 7 x ^ { 2 } + 2 x - 14$ 
B)  $f ( x ) = x ^ { 3 } + 7 x ^ { 2 } - 2 x - 14$ 
C)  $f ( x ) = x ^ { 3 } + 7 x ^ { 2 } - 2 x + 14$ 
D)  $f ( x ) = x ^ { 3 } - 7 x ^ { 2 } - 2 x - 14$

Question 19

Describe the strength and direction of the linear correlation.
-

Accepted Answer

A)  Little or no linear correlation 
B)  Weak negative linear correlation 
C)  Strong positive linear correlation 
D)  Strong negative linear correlation 
A)  Little or no linear correlation 
B)  Weak negative linear correlation 
C)  Strong positive linear correlation 
D)  Strong negative linear correlation

Question 20

Use a cubic or quartic regression (as specified) to fit a curve through the points given in the table. Round to the nearest
hundredth.
-

Accepted Answer

A)  $y \approx 0.16 x ^ { 4 } + 3.77 x ^ { 3 } + 20.02 x ^ { 2 } + 51.93 x - 44.00$ 
B)  $y \approx - 0.18 x ^ { 4 } + 3.77 x ^ { 3 } - 20.02 x ^ { 2 } + 41.93 x - 44.00$ 
C)  $y \approx - 0.18 x ^ { 4 } + 3.27 x ^ { 3 } + 20.02 x ^ { 2 } + 55.93 x - 46.00$ 
D)  $y \approx - 0.18 x ^ { 4 } + 3.27 x ^ { 3 } - 20.02 x ^ { 2 } + 51.93 x - 44.00$ 
A)  $y \approx 0.16 x ^ { 4 } + 3.77 x ^ { 3 } + 20.02 x ^ { 2 } + 51.93 x - 44.00$ 
B)  $y \approx - 0.18 x ^ { 4 } + 3.77 x ^ { 3 } - 20.02 x ^ { 2 } + 41.93 x - 44.00$ 
C)  $y \approx - 0.18 x ^ { 4 } + 3.27 x ^ { 3 } + 20.02 x ^ { 2 } + 55.93 x - 46.00$ 
D)  $y \approx - 0.18 x ^ { 4 } + 3.27 x ^ { 3 } - 20.02 x ^ { 2 } + 51.93 x - 44.00$

Find all rational zeros. - $f ( x ) = x ^ { 4 } - 7 x ^ { 3 } + 3 x ^ { 2 } + 21 x - 18$

Find the remainder when f(x) is divided by (x - k) - $f ( x ) = 9 x ^ { 4 } + 8 x ^ { 3 } + 2 x ^ { 2 } - 4 x + 58 ; k = 3$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $\frac { 5 - x } { x } + \frac { 3 } { 4 } = \frac { 7 } { x }$

Match the equation to one of the curves (for x ≥ 0). - $f ( x ) = 2.7 x ^ { 2 / 3 }$ $Match the equation to one of the curves (for x ≥ 0). - f ( x ) = 2.7 x ^ { 2 / 3 }$

Find the requested function. -Find the cubic function with the given table of values.

Solve the inequality. - $3 + \frac { 14 } { x } - \frac { 5 } { x ^ { 2 } } \leq 0$

Find the vertex of the graph of the function. - $f ( x ) = 3 ( x - \sqrt { 5 } ) ^ { 2 } + 5$

State the power and constant of variation for the function, and then analyze it. - $f ( x ) = - 4 x ^ { 1 / 3 }$

Solve the problem. -Find the remainder when $x ^ { 49 } - 10$ is divided by $x + 1$ .

Use a graphing calculator to approximate the real zeros of the function defined by f(x). Express decimal approximations to the nearest hundredth. - $f ( x ) = x ^ { 4 } - 2.44 x ^ { 3 } - 12.25 x ^ { 2 } + 21.56 x + 17.68$

List the x- and y-intercepts, and graph the function. - $f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } - x - 20 }$ $List the x- and y-intercepts, and graph the function. - f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } - x - 20 }$

Match the equation to one of the curves (for x ≥ 0). - $f ( x ) = \frac { 1 } { 3 } x ^ { - 5 }$ $Match the equation to one of the curves (for x ≥ 0). - f ( x ) = \frac { 1 } { 3 } x ^ { - 5 }$

Describe the end behavior of the polynomial function by finding $Describe the end behavior of the polynomial function by finding - f ( x ) = x ^ { 3 } + x ^ { 4 } - 6 x ^ { 2 } - 7 x + 1$ - $f ( x ) = x ^ { 3 } + x ^ { 4 } - 6 x ^ { 2 } - 7 x + 1$

Write an equation for the quadratic function whose graph contains the given vertex and point. -Vertex $( 3 , - 2 )$ , point $( 0,25 )$

Match the given graph with its polynomial function.Choose the one alternative that best completes the statement or answers the question. -

Divide f(x) by d(x), and write a summary statement in the form indicated. - $f ( x ) = x ^ { 2 } - 2 x + 5 ; d ( x ) = x - 7 \quad$ (Write answer in fraction form)

Determine if the function is a power function. If it is, then state the power and constant of variation. - $f ( x ) = \frac { 1 } { 3 } x ^ { 2 }$

Find a cubic function with the given zeros. - $\sqrt { 2 } , - \sqrt { 2 } , - 7$

Describe the strength and direction of the linear correlation. -

Use a cubic or quartic regression (as specified) to fit a curve through the points given in the table. Round to the nearest hundredth. -

Functions and Graphs

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

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Exam 2: Polynomial, Power, and Rational Functions

Find all rational zeros. - f(x)=x4−7x3+3x2+21x−18f ( x ) = x ^ { 4 } - 7 x ^ { 3 } + 3 x ^ { 2 } + 21 x - 18f(x)=x4−7x3+3x2+21x−18

Find the remainder when f(x) is divided by (x - k) - f(x)=9x4+8x3+2x2−4x+58;k=3f ( x ) = 9 x ^ { 4 } + 8 x ^ { 3 } + 2 x ^ { 2 } - 4 x + 58 ; k = 3f(x)=9x4+8x3+2x2−4x+58;k=3

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - 5−xx+34=7x\frac { 5 - x } { x } + \frac { 3 } { 4 } = \frac { 7 } { x }x5−x​+43​=x7​

Match the equation to one of the curves (for x ≥ 0). - f(x)=2.7x2/3f ( x ) = 2.7 x ^ { 2 / 3 }f(x)=2.7x2/3