Question 1

Solve the problem.

-Which of the following polynomial functions might have the graph shown in the illustration below?

Accepted Answer

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

Question 2

Use the graph of a power function and transformations to sketch the graph of the polynomial function.

-$$f ( x ) = \frac { 1 } { 2 } ( x - 4 ) ^ { 5 } + 3$$

Accepted Answer

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

Question 3

Solve the variation problem.
-The volume $\mathrm { V }$ of a given mass of gas varies directly as the temperature $\mathrm { T }$ and inversely as the pressure P. A measuring device is calibrated to give $\mathrm { V } = 258 \mathrm { in } ^ { 3 }$ when $\mathrm { T } = 430 ^ { \circ } \mathrm { C }$ and $\mathrm { P } = 25 \mathrm { lb } /$ in $^ { 2 }$. What is the volume on this device when the temperature is $150 ^ { \circ } \mathrm { C }$ and the pressure is $20 \mathrm { lb } / \mathrm { in } ^ { 2 }$ ?

Accepted Answer

A) 7.5 cubic inches 
B) 122.5 cubic inches 
C) 102.5 cubic inches 
D) 112.5 cubic inches 
A) 7.5 cubic inches 
B) 122.5 cubic inches 
C) 102.5 cubic inches 
D) 112.5 cubic inches

Question 4

Form a polynomial f(x)with real coefficients having the given degree and zeros.
-Degree: 3; zeros: $- 4$ and $3 - 2 \mathrm { i }$

Accepted Answer

A)  $f ( x ) = x ^ { 3 } - x ^ { 2 } - 11 x + 52$ 
B)  $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } + 5 x - 52$ 
C)  $f ( x ) = x ^ { 3 } - x ^ { 2 } + 11 x + 52$ 
D)  $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 11 x + 52$ 
A)  $f ( x ) = x ^ { 3 } - x ^ { 2 } - 11 x + 52$ 
B)  $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } + 5 x - 52$ 
C)  $f ( x ) = x ^ { 3 } - x ^ { 2 } + 11 x + 52$ 
D)  $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 11 x + 52$

Question 5

Sketch the graph of the polynomial function.
-

Accepted Answer

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

Question 6

Find the remaining zeros of f(x)given that c is a zero. Then rewrite f(x)in completely factored form.
-$f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 9 x - 18 ; c = 3$ is a zero

Accepted Answer

A)  $- 3 , - 2 ; f ( x ) = ( x + 3 ) ( x + 2 ) ( x - 3 )$ 
B)  $- 3,2,3 ; f ( x ) = ( x + 3 ) ( x - 2 ) ( x - 3 )$ 
C)  $- 2 ; f ( x ) = ( x + 2 ) \left( x ^ { 2 } + x - 9 \right)$ 
D)  $- 3 ; f ( x ) = ( x + 3 ) \left( x ^ { 2 } - x - 6 \right)$ 
A)  $- 3 , - 2 ; f ( x ) = ( x + 3 ) ( x + 2 ) ( x - 3 )$ 
B)  $- 3,2,3 ; f ( x ) = ( x + 3 ) ( x - 2 ) ( x - 3 )$ 
C)  $- 2 ; f ( x ) = ( x + 2 ) \left( x ^ { 2 } + x - 9 \right)$ 
D)  $- 3 ; f ( x ) = ( x + 3 ) \left( x ^ { 2 } - x - 6 \right)$

Question 7

Find the axis of symmetry of the quadratic function.
-$$f ( x ) = - ( x + 3 ) ^ { 2 } + 9$$

Accepted Answer

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

Question 8

Solve the problem.
-The owner of a video store has determined that the cost C, in dollars, of operating the store is approximately given by $$C ( x ) = 2 x ^ { 2 } - 28 x + 600$$ , where x is the number of videos rented daily. Find the lowest cost to the nearest dollar.

Accepted Answer

A) $698 
B) $502 
C) $208 
D) $404 
A) $698 
B) $502 
C) $208 
D) $404

Question 9

Use the graph of a power function and transformations to sketch the graph of the polynomial function.

-$$f ( x ) = ( x + 5 ) ^ { 4 } + 3$$

Accepted Answer

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

Question 10

Use synthetic division to divide f(x)by x - c, and then write f(x)in the form f(x)= (x - c)q(x)+ r.
-$$f ( x ) = x ^ { 3 } - x ^ { 2 } + 3 ; x + 2$$

Accepted Answer

A)  $( x + 2 ) \left( 3 x ^ { 2 } - 4 x + 2 \right) + 0$ 
B)  $( x + 2 ) \left( x ^ { 2 } - 3 x + 6 \right) + 2$ 
C)  $( x + 2 ) \left( x ^ { 2 } + x + 2 \right) - 9$ 
D)  $( x + 2 ) \left( x ^ { 2 } - 3 x + 6 \right) - 9$ 
A)  $( x + 2 ) \left( 3 x ^ { 2 } - 4 x + 2 \right) + 0$ 
B)  $( x + 2 ) \left( x ^ { 2 } - 3 x + 6 \right) + 2$ 
C)  $( x + 2 ) \left( x ^ { 2 } + x + 2 \right) - 9$ 
D)  $( x + 2 ) \left( x ^ { 2 } - 3 x + 6 \right) - 9$

Question 11

Use the end behavior of the graph of the polynomial function to determine whether the degree is even or odd and determine whether the leading coefficient is positive or negative.
-

Accepted Answer

A) even; negative 
B) odd; negative 
C) even; positive 
D) odd; positive 
A) even; negative 
B) odd; negative 
C) even; positive 
D) odd; positive

Question 12

Use the graph of a power function and transformations to sketch the graph of the polynomial function.

-

Accepted Answer

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

Question 13

Find the domain of the rational function.
-$$f ( x ) = \frac { x + 6 } { x ^ { 4 } - 4 }$$

Accepted Answer

A)  $\{ x \mid x \neq 0 , x \neq 4 \}$ 
B)  $\{ x \mid x \neq - 2 , x \neq 2 \}$ 
C)  all real numbers 
D)  $\{ x \mid x \neq - 2 , x \neq 2 , x \neq - 6 \}$ 
A)  $\{ x \mid x \neq 0 , x \neq 4 \}$ 
B)  $\{ x \mid x \neq - 2 , x \neq 2 \}$ 
C)  all real numbers 
D)  $\{ x \mid x \neq - 2 , x \neq 2 , x \neq - 6 \}$

Question 14

Solve the problem.
-The owner of a video store has determined that the profits P of the store are approximately given by $$P ( x ) = - x ^ { 2 } + 50 x + 62$$ where x is the number of videos rented daily. Find the maximum profit to the nearest dollar.

Accepted Answer

A) $1312 
B) $625 
C) $1250 
D) $687 
A) $1312 
B) $625 
C) $1250 
D) $687

Question 15

Determine the end behavior, the y-intercept, all real zeros, and at least one test value between each intercept. Then connect the points with a smooth curve.
-

Accepted Answer

The answer of Determine the end behavior, the y-intercept, all...

Question 16

Form a polynomial f(x)with real coefficients having the given degree and zeros.
-Degree: 4 ; zeros: $2 \mathrm { i }$ and $- 4 \mathrm { i }$

Accepted Answer

A)  $f ( x ) = x ^ { 4 } - 4 x ^ { 2 } + 64$ 
B)  $f ( x ) = x ^ { 4 } + 20 x ^ { 2 } - 4 x + 64$ 
C)  $f ( x ) = x ^ { 4 } + 20 x ^ { 2 } + 64$ 
D)  $f ( x ) = x ^ { 4 } - 2 x ^ { 3 } + 20 x ^ { 2 } + 64$ 
A)  $f ( x ) = x ^ { 4 } - 4 x ^ { 2 } + 64$ 
B)  $f ( x ) = x ^ { 4 } + 20 x ^ { 2 } - 4 x + 64$ 
C)  $f ( x ) = x ^ { 4 } + 20 x ^ { 2 } + 64$ 
D)  $f ( x ) = x ^ { 4 } - 2 x ^ { 3 } + 20 x ^ { 2 } + 64$

Question 17

Find the range of the quadratic function in interval notation.
-$$f ( x ) = - ( x + 4 ) ^ { 2 } + 5$$

Accepted Answer

A)  $( - \infty , 4 ]$ 
B)  $( - \infty , 5 ]$ 
C)  $[ - 4 , \infty )$ 
D)  $[ 5 , \infty )$ 
A)  $( - \infty , 4 ]$ 
B)  $( - \infty , 5 ]$ 
C)  $[ - 4 , \infty )$ 
D)  $[ 5 , \infty )$

Question 18

Form a polynomial f(x)with real coefficients having the given degree and zeros.
-Degree 3: zeros: 1 + i and -5

Accepted Answer

A)  $f ( x ) = x ^ { 3 } - 5 x ^ { 2 } - 8 x - 12$ 
B)  $f ( x ) = x ^ { 3 } + x ^ { 2 } - 8 x + 10$ 
C)  $f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 8 x + 10$ 
D)  $f ( x ) = x ^ { 3 } + 3 x ^ { 2 } + 10 x - 8$ 
A)  $f ( x ) = x ^ { 3 } - 5 x ^ { 2 } - 8 x - 12$ 
B)  $f ( x ) = x ^ { 3 } + x ^ { 2 } - 8 x + 10$ 
C)  $f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 8 x + 10$ 
D)  $f ( x ) = x ^ { 3 } + 3 x ^ { 2 } + 10 x - 8$

Question 19

Graph the quadratic function using its vertex, axis of symmetry, and intercepts.
-$$f ( x ) = x ^ { 2 } + 12 x + 36$$

Accepted Answer

A)  vertex $( - 6,0 )$
intercepts $( 0,36 ) , ( - 6,0 )$
  
B)  vertex $( - 6,36 )$
intercept $( 0,72 )$
  
C)  vertex $( 6,0 )$
intercepts $( 0,36 ) , ( 6,0 )$
  
D)  vertex $( 6,36 )$
intercept $( 0,72 )$
  
A)  vertex $( - 6,0 )$
intercepts $( 0,36 ) , ( - 6,0 )$
  
B)  vertex $( - 6,36 )$
intercept $( 0,72 )$
  
C)  vertex $( 6,0 )$
intercepts $( 0,36 ) , ( 6,0 )$
  
D)  vertex $( 6,36 )$
intercept $( 0,72 )$

Question 20

Use the end behavior of the graph of the polynomial function to determine whether the degree is even or odd and determine whether the leading coefficient is positive or negative.
-

Accepted Answer

A) odd; positive 
B) odd; negative 
C) even; positive 
D) even; negative 
A) odd; positive 
B) odd; negative 
C) even; positive 
D) even; negative

Solve the problem. -Which of the following polynomial functions might have the graph shown in the illustration below?

Form a polynomial f(x)with real coefficients having the given degree and zeros. -Degree: 3; zeros: $- 4$ and $3 - 2 \mathrm { i }$

Sketch the graph of the polynomial function. -

Find the remaining zeros of f(x)given that c is a zero. Then rewrite f(x)in completely factored form. - $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 9 x - 18 ; c = 3$ is a zero

Find the axis of symmetry of the quadratic function. - $f ( x ) = - ( x + 3 ) ^ { 2 } + 9$

Solve the problem. -The owner of a video store has determined that the cost C, in dollars, of operating the store is approximately given by $C ( x ) = 2 x ^ { 2 } - 28 x + 600$ , where x is the number of videos rented daily. Find the lowest cost to the nearest dollar.

Use the graph of a power function and transformations to sketch the graph of the polynomial function. - $f ( x ) = ( x + 5 ) ^ { 4 } + 3$ $Use the graph of a power function and transformations to sketch the graph of the polynomial function. - f ( x ) = ( x + 5 ) ^ { 4 } + 3$

Use synthetic division to divide f(x)by x - c, and then write f(x)in the form f(x)= (x - c)q(x)+ r. - $f ( x ) = x ^ { 3 } - x ^ { 2 } + 3 ; x + 2$

Use the end behavior of the graph of the polynomial function to determine whether the degree is even or odd and determine whether the leading coefficient is positive or negative. -

Use the graph of a power function and transformations to sketch the graph of the polynomial function. -

Find the domain of the rational function. - $f ( x ) = \frac { x + 6 } { x ^ { 4 } - 4 }$

Solve the problem. -The owner of a video store has determined that the profits P of the store are approximately given by $P ( x ) = - x ^ { 2 } + 50 x + 62$ where x is the number of videos rented daily. Find the maximum profit to the nearest dollar.

Determine the end behavior, the y-intercept, all real zeros, and at least one test value between each intercept. Then connect the points with a smooth curve. -

Form a polynomial f(x)with real coefficients having the given degree and zeros. -Degree: 4 ; zeros: $2 \mathrm { i }$ and $- 4 \mathrm { i }$

Find the range of the quadratic function in interval notation. - $f ( x ) = - ( x + 4 ) ^ { 2 } + 5$

Form a polynomial f(x)with real coefficients having the given degree and zeros. -Degree 3: zeros: 1 + i and -5

Graph the quadratic function using its vertex, axis of symmetry, and intercepts. - $f ( x ) = x ^ { 2 } + 12 x + 36$ $Graph the quadratic function using its vertex, axis of symmetry, and intercepts. - f ( x ) = x ^ { 2 } + 12 x + 36$

Use the end behavior of the graph of the polynomial function to determine whether the degree is even or odd and determine whether the leading coefficient is positive or negative. -

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Exam 4: Polynomial and Rational Functions

Solve the problem. -Which of the following polynomial functions might have the graph shown in the illustration below?

Use the graph of a power function and transformations to sketch the graph of the polynomial function. - f(x)=12(x−4)5+3f ( x ) = \frac { 1 } { 2 } ( x - 4 ) ^ { 5 } + 3f(x)=21​(x−4)5+3

Form a polynomial f(x)with real coefficients having the given degree and zeros. -Degree: 3; zeros: −4- 4−4 and 3−2i3 - 2 \mathrm { i }3−2i

Sketch the graph of the polynomial function. -

Find the remaining zeros of f(x)given that c is a zero. Then rewrite f(x)in completely factored form. - f(x)=x3+2x2−9x−18;c=3f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 9 x - 18 ; c = 3f(x)=x3+2x2−9x−18;c=3 is a zero

Find the axis of symmetry of the quadratic function. - f(x)=−(x+3)2+9f ( x ) = - ( x + 3 ) ^ { 2 } + 9f(x)=−(x+3)2+9

Use the graph of a power function and transformations to sketch the graph of the polynomial function. - f(x)=(x+5)4+3f ( x ) = ( x + 5 ) ^ { 4 } + 3f(x)=(x+5)4+3

Use synthetic division to divide f(x)by x - c, and then write f(x)in the form f(x)= (x - c)q(x)+ r. - f(x)=x3−x2+3;x+2f ( x ) = x ^ { 3 } - x ^ { 2 } + 3 ; x + 2f(x)=x3−x2+3;x+2

Use the end behavior of the graph of the polynomial function to determine whether the degree is even or odd and determine whether the leading coefficient is positive or negative. -

Use the graph of a power function and transformations to sketch the graph of the polynomial function. -

Find the domain of the rational function. - f(x)=x+6x4−4f ( x ) = \frac { x + 6 } { x ^ { 4 } - 4 }f(x)=x4−4x+6​

Solve the problem. -The owner of a video store has determined that the profits P of the store are approximately given by P(x)=−x2+50x+62P ( x ) = - x ^ { 2 } + 50 x + 62P(x)=−x2+50x+62 where x is the number of videos rented daily. Find the maximum profit to the nearest dollar.

Determine the end behavior, the y-intercept, all real zeros, and at least one test value between each intercept. Then connect the points with a smooth curve. -

Form a polynomial f(x)with real coefficients having the given degree and zeros. -Degree: 4 ; zeros: 2i2 \mathrm { i }2i and −4i- 4 \mathrm { i }−4i

Find the range of the quadratic function in interval notation. - f(x)=−(x+4)2+5f ( x ) = - ( x + 4 ) ^ { 2 } + 5f(x)=−(x+4)2+5

Form a polynomial f(x)with real coefficients having the given degree and zeros. -Degree 3: zeros: 1 + i and -5

Graph the quadratic function using its vertex, axis of symmetry, and intercepts. - f(x)=x2+12x+36f ( x ) = x ^ { 2 } + 12 x + 36f(x)=x2+12x+36

Use the end behavior of the graph of the polynomial function to determine whether the degree is even or odd and determine whether the leading coefficient is positive or negative. -

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Form a polynomial f(x)with real coefficients having the given degree and zeros. -Degree: 3; zeros: $- 4$ and $3 - 2 \mathrm { i }$

Find the remaining zeros of f(x)given that c is a zero. Then rewrite f(x)in completely factored form. - $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 9 x - 18 ; c = 3$ is a zero

Find the axis of symmetry of the quadratic function. - $f ( x ) = - ( x + 3 ) ^ { 2 } + 9$

Use the graph of a power function and transformations to sketch the graph of the polynomial function. - $f ( x ) = ( x + 5 ) ^ { 4 } + 3$ $Use the graph of a power function and transformations to sketch the graph of the polynomial function. - f ( x ) = ( x + 5 ) ^ { 4 } + 3$

Use synthetic division to divide f(x)by x - c, and then write f(x)in the form f(x)= (x - c)q(x)+ r. - $f ( x ) = x ^ { 3 } - x ^ { 2 } + 3 ; x + 2$

Find the domain of the rational function. - $f ( x ) = \frac { x + 6 } { x ^ { 4 } - 4 }$

Solve the problem. -The owner of a video store has determined that the profits P of the store are approximately given by $P ( x ) = - x ^ { 2 } + 50 x + 62$ where x is the number of videos rented daily. Find the maximum profit to the nearest dollar.

Form a polynomial f(x)with real coefficients having the given degree and zeros. -Degree: 4 ; zeros: $2 \mathrm { i }$ and $- 4 \mathrm { i }$

Find the range of the quadratic function in interval notation. - $f ( x ) = - ( x + 4 ) ^ { 2 } + 5$

Graph the quadratic function using its vertex, axis of symmetry, and intercepts. - $f ( x ) = x ^ { 2 } + 12 x + 36$ $Graph the quadratic function using its vertex, axis of symmetry, and intercepts. - f ( x ) = x ^ { 2 } + 12 x + 36$