Question 1

Use the remainder theorem to find the remainder when f(x)is divided by x - c.
-$$f ( x ) = x ^ { 4 } + 8 x ^ { 3 } + 12 x ^ { 2 } ; x + 1$$

Accepted Answer

A) 5 
B) -21 
C) -5 
D) 21 
A) 5 
B) -21 
C) -5 
D) 21

Question 2

State whether the function is a polynomial function or not. If it is, give its degree.

-$$f ( x ) = 12 x ^ { 4 } - 2 x ^ { 3 } + 2$$

Accepted Answer

A) Yes; degree 7 
B) Not a polynomial 
C) Yes; degree 4 
D) Yes; degree 8 
A) Yes; degree 7 
B) Not a polynomial 
C) Yes; degree 4 
D) Yes; degree 8

Question 3

Solve the problem.
-You have 80 feet of fencing to enclose a rectangular region. What is the maximum area?

Accepted Answer

A)  $6400 \mathrm { ft } ^ { 2 }$ 
B)  $400 \mathrm { ft } ^ { 2 }$ 
C)  $1600 \mathrm { ft } ^ { 2 }$ 
D)  $396 \mathrm { ft } ^ { 2 }$ 
A)  $6400 \mathrm { ft } ^ { 2 }$ 
B)  $400 \mathrm { ft } ^ { 2 }$ 
C)  $1600 \mathrm { ft } ^ { 2 }$ 
D)  $396 \mathrm { ft } ^ { 2 }$

Question 4

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

Accepted Answer

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

Question 5

Use the Factor Theorem to determine whether x - c is a factor of f(x).
-$$f ( x ) = 7 x ^ { 3 } + 26 x ^ { 2 } - 7 x - 4 ; x + 4$$

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 6

For the following rational function, identify the coordinates of all removable discontinuities and sketch the graph. Identify all intercepts and find the equations of all asymptotes.
-$$f ( x ) = \frac { x ^ { 2 } - 16 } { x - 4 }$$

Accepted Answer

A)  removable discontinuity at $( - 4 , - 8 )$;
 no $x$-intercepts, $y$-intercept: $\left( 0 , - \frac { 1 } { 16 } \right)$
asymptotes: $y = 0$ and $x = 4$ 
  
B)  removable discontinuity at $( 4,8 )$; 
x-intercept: $( - 4,0 )$, y-intercept: $( 0,4 )$; 
no asymptotes
  
C)  removable discontinuity at $( 4,8 )$;
no $x$-intercepts, $y$-intercept: $\left( 0 , \frac { 1 } { 16 } \right)$
asymptotes: $\mathrm { y } = 0$ and $\mathrm { x } = 4$
  
D)  removable discontinuity at $( - 4 , - 8 )$;  
no $x$-intercept: $( 4,0 )$, y-intercept: $( 0 , - 4 )$; asymptotes: $\mathrm { y } = 0$ and $\mathrm { x } = 4$ 
no asymptotes
  
A)  removable discontinuity at $( - 4 , - 8 )$;
 no $x$-intercepts, $y$-intercept: $\left( 0 , - \frac { 1 } { 16 } \right)$
asymptotes: $y = 0$ and $x = 4$ 
  
B)  removable discontinuity at $( 4,8 )$; 
x-intercept: $( - 4,0 )$, y-intercept: $( 0,4 )$; 
no asymptotes
  
C)  removable discontinuity at $( 4,8 )$;
no $x$-intercepts, $y$-intercept: $\left( 0 , \frac { 1 } { 16 } \right)$
asymptotes: $\mathrm { y } = 0$ and $\mathrm { x } = 4$
  
D)  removable discontinuity at $( - 4 , - 8 )$;  
no $x$-intercept: $( 4,0 )$, y-intercept: $( 0 , - 4 )$; asymptotes: $\mathrm { y } = 0$ and $\mathrm { x } = 4$ 
no asymptotes

Question 7

State whether the function is a polynomial function or not. If it is, give its degree.

-f(x)= 6

Accepted Answer

A) Yes; degree 1 
B) Yes; degree 0 
C) Not a polynomial 
D) Yes; degree 6 
A) Yes; degree 1 
B) Yes; degree 0 
C) Not a polynomial 
D) Yes; degree 6

Question 8

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

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

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

Write the equation of the function in the form f(x)= ax2 + bx + c.
-

Accepted Answer

A)  $y = - 2 ( x + 2 ) ^ { 2 } - 6$ 
B)  $y = \frac { 1 } { 2 } ( x + 2 ) ^ { 2 } + 6$ 
C)  $y = - \frac { 1 } { 2 } ( x + 2 ) ^ { 2 } - 6$ 
D)  $y = 2 ( x + 2 ) ^ { 2 } + 6$ 
A)  $y = - 2 ( x + 2 ) ^ { 2 } - 6$ 
B)  $y = \frac { 1 } { 2 } ( x + 2 ) ^ { 2 } + 6$ 
C)  $y = - \frac { 1 } { 2 } ( x + 2 ) ^ { 2 } - 6$ 
D)  $y = 2 ( x + 2 ) ^ { 2 } + 6$

Question 11

For the following rational function, identify the coordinates of all removable discontinuities and sketch the graph. Identify all intercepts and find the equations of all asymptotes.
-$$f ( x ) = \frac { \left( x ^ { 2 } - 9 \right) ( x + 5 ) } { \left( x ^ { 2 } - 25 \right) ( x + 3 ) }$$

Accepted Answer

A)  removable discontinuity at $( - 3,0 )$;
 $x$-intercept: $( - 3,0 ) , y$-intercept: $\left( 0 , \frac { 3 } { 5 } \right)$
asymptotes: $x = - 5 , y = 1$

B)  removable discontinuity at $( - 3 , - 3 )$;
 $x$-intercept: $( 3,0 ) , y$-intercept: $\left( 0 , - \frac { 3 } { 5 } \right) ;$ 
asymptotes: $x = - 5 , y = 1$
  
C)  removable discontinuities: $\left( - 5 , \frac { 4 } { 5 } \right) , \left( - 3 , \frac { 3 } { 4 } \right)$
$x$-intercept: $( 3,0 ) , y$-intercept: $\left( 0 , \frac { 3 } { 5 } \right)$
asymptotes: $x = 5 , y = 1$ 
  
D)  removable discontinuities: $\left( - 5 , \frac { 1 } { 5 } \right) , ( - 3,0 )$;  $x$-intercept: $( - 3,0 ) , y$-intercept: $\left( 0 , - \frac { 3 } { 5 } \right)$ 
asymptotes: $x = 5 , y = 1$
  
A)  removable discontinuity at $( - 3,0 )$;
 $x$-intercept: $( - 3,0 ) , y$-intercept: $\left( 0 , \frac { 3 } { 5 } \right)$
asymptotes: $x = - 5 , y = 1$

B)  removable discontinuity at $( - 3 , - 3 )$;
 $x$-intercept: $( 3,0 ) , y$-intercept: $\left( 0 , - \frac { 3 } { 5 } \right) ;$ 
asymptotes: $x = - 5 , y = 1$
  
C)  removable discontinuities: $\left( - 5 , \frac { 4 } { 5 } \right) , \left( - 3 , \frac { 3 } { 4 } \right)$
$x$-intercept: $( 3,0 ) , y$-intercept: $\left( 0 , \frac { 3 } { 5 } \right)$
asymptotes: $x = 5 , y = 1$ 
  
D)  removable discontinuities: $\left( - 5 , \frac { 1 } { 5 } \right) , ( - 3,0 )$;  $x$-intercept: $( - 3,0 ) , y$-intercept: $\left( 0 , - \frac { 3 } { 5 } \right)$ 
asymptotes: $x = 5 , y = 1$

Question 12

Use the Factor Theorem to determine whether x - c is a factor of f(x).
-$$f ( x ) = 7 x ^ { 3 } + 33 x ^ { 2 } - 9 x + 5 ; x + 5$$

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 13

Use the Factor Theorem to determine whether x - c is a factor of f(x).
-$$f ( x ) = 8 x ^ { 4 } + 23 x ^ { 3 } - 3 x ^ { 2 } + x + 3 ; x + 3$$

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 14

Rewrite the quadratic function in standard form by completing the square.
-$$f ( x ) = x ^ { 2 } - 18 x$$

Accepted Answer

A)  $f ( x ) = ( x + 18 ) ^ { 2 } - 18$ 
B)  $f ( x ) = ( x - 18 ) ^ { 2 } - 324$ 
C)  $f ( x ) = ( x + 9 ) ^ { 2 } - 9$ 
D)  $f ( x ) = ( x - 9 ) ^ { 2 } - 81$ 
A)  $f ( x ) = ( x + 18 ) ^ { 2 } - 18$ 
B)  $f ( x ) = ( x - 18 ) ^ { 2 } - 324$ 
C)  $f ( x ) = ( x + 9 ) ^ { 2 } - 9$ 
D)  $f ( x ) = ( x - 9 ) ^ { 2 } - 81$

Question 15

Solve the problem.
-A projectile is fired from a cliff 200 feet above the water at an inclination of $45 ^ { \circ }$ to the horizontal, with a muzzle velocity of 380 feet per second. The height h of the projectile above the water is given by h $( x ) = \frac { - 32 x ^ { 2 } } { ( 380 ) ^ { 2 } } + x + 200$, where $x$ is the horizontal distance of the projectile from the base of the cliff. Find the maximum height of the projectile.

Accepted Answer

A) 2256.25 ft 
B) 3584.38 ft 
C) 1128.13 ft 
D) 1328.13 ft 
A) 2256.25 ft 
B) 3584.38 ft 
C) 1128.13 ft 
D) 1328.13 ft

Question 16

First rewrite the quadratic function in standard form by completing the square, then find any x-intercepts and any y-intercepts.
-$$f ( x ) = - 9 x ^ { 2 } - 2 x - 12$$

Accepted Answer

A)  No x-intercepts; No $y$-intercepts 
B)  x-intercepts: $- \frac { 1 } { 9 }$ and $- \frac { 107 } { 9 } ; y$-intercept: 12 
C)  $x$-intercepts: $\frac { 1 } { 9 }$ and $\frac { 107 } { 9 } ; y$-intercept: $- 12$ 
D)  No $x$-intercepts; $y$-intercept: $- 12$ 
A)  No x-intercepts; No $y$-intercepts 
B)  x-intercepts: $- \frac { 1 } { 9 }$ and $- \frac { 107 } { 9 } ; y$-intercept: 12 
C)  $x$-intercepts: $\frac { 1 } { 9 }$ and $\frac { 107 } { 9 } ; y$-intercept: $- 12$ 
D)  No $x$-intercepts; $y$-intercept: $- 12$

Question 17

Find the coordinates of the vertex of the quadratic function.
-$$f ( x ) = - 4 x ^ { 2 } - 8 x - 9$$

Accepted Answer

A)  $( 1 , - 21 )$ 
B)  $( 2 , - 41 )$ 
C)  $( - 2 , - 17 )$ 
D)  $( - 1 , - 5 )$ 
A)  $( 1 , - 21 )$ 
B)  $( 2 , - 41 )$ 
C)  $( - 2 , - 17 )$ 
D)  $( - 1 , - 5 )$

Question 18

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.
-$$f ( x ) = x ^ { 5 } - 3 x ^ { 4 } - 7 x ^ { 3 } - 12 x ^ { 2 } - 13 x - 7 ; x - 5$$

Accepted Answer

A)  $( x - 5 ) \left( x ^ { 4 } + 2 x ^ { 3 } + 3 x ^ { 2 } + 3 x + 2 \right) + 3$ 
B)  $( x - 5 ) \left( x ^ { 4 } + 2 x ^ { 3 } + 3 x ^ { 2 } + 3 x + 3 \right) + 0$ 
C)  $( x - 5 ) \left( x ^ { 3 } + 2 x ^ { 2 } + 3 x + 3 \right) + 3$ 
D)  $( x - 5 ) \left( x ^ { 4 } + 2 x ^ { 3 } + 3 x ^ { 2 } + 3 x - 2 \right) + 5$ 
A)  $( x - 5 ) \left( x ^ { 4 } + 2 x ^ { 3 } + 3 x ^ { 2 } + 3 x + 2 \right) + 3$ 
B)  $( x - 5 ) \left( x ^ { 4 } + 2 x ^ { 3 } + 3 x ^ { 2 } + 3 x + 3 \right) + 0$ 
C)  $( x - 5 ) \left( x ^ { 3 } + 2 x ^ { 2 } + 3 x + 3 \right) + 3$ 
D)  $( x - 5 ) \left( x ^ { 4 } + 2 x ^ { 3 } + 3 x ^ { 2 } + 3 x - 2 \right) + 5$

Question 19

Sketch the graph of the polynomial function.
-

Accepted Answer

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

Question 20

Find the x- and y-intercepts of f.
-$$f ( x ) = - x ^ { 2 } ( x + 5 ) \left( x ^ { 2 } - 1 \right)$$

Accepted Answer

A) x-intercepts: -5, 0, 1; y-intercept: -5 
B) x-intercepts: -1, 0, 1, 5; y-intercept: 0 
C) x-intercepts: -5, -1, 0, 1; y-intercept: -5 
D) x-intercepts: -5, -1, 0, 1; y-intercept: 0 
A) x-intercepts: -5, 0, 1; y-intercept: -5 
B) x-intercepts: -1, 0, 1, 5; y-intercept: 0 
C) x-intercepts: -5, -1, 0, 1; y-intercept: -5 
D) x-intercepts: -5, -1, 0, 1; y-intercept: 0

Use the remainder theorem to find the remainder when f(x)is divided by x - c. - $f ( x ) = x ^ { 4 } + 8 x ^ { 3 } + 12 x ^ { 2 } ; x + 1$

State whether the function is a polynomial function or not. If it is, give its degree. - $f ( x ) = 12 x ^ { 4 } - 2 x ^ { 3 } + 2$

Solve the problem. -You have 80 feet of fencing to enclose a rectangular region. What is the maximum area?

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

Use the Factor Theorem to determine whether x - c is a factor of f(x). - $f ( x ) = 7 x ^ { 3 } + 26 x ^ { 2 } - 7 x - 4 ; x + 4$

State whether the function is a polynomial function or not. If it is, give its degree. -f(x)= 6

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

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

Write the equation of the function in the form f(x)= ax2 + bx + c. -

Use the Factor Theorem to determine whether x - c is a factor of f(x). - $f ( x ) = 7 x ^ { 3 } + 33 x ^ { 2 } - 9 x + 5 ; x + 5$

Use the Factor Theorem to determine whether x - c is a factor of f(x). - $f ( x ) = 8 x ^ { 4 } + 23 x ^ { 3 } - 3 x ^ { 2 } + x + 3 ; x + 3$

Rewrite the quadratic function in standard form by completing the square. - $f ( x ) = x ^ { 2 } - 18 x$

First rewrite the quadratic function in standard form by completing the square, then find any x-intercepts and any y-intercepts. - $f ( x ) = - 9 x ^ { 2 } - 2 x - 12$

Find the coordinates of the vertex of the quadratic function. - $f ( x ) = - 4 x ^ { 2 } - 8 x - 9$

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. - $f ( x ) = x ^ { 5 } - 3 x ^ { 4 } - 7 x ^ { 3 } - 12 x ^ { 2 } - 13 x - 7 ; x - 5$

Sketch the graph of the polynomial function. -

Find the x- and y-intercepts of f. - $f ( x ) = - x ^ { 2 } ( x + 5 ) \left( x ^ { 2 } - 1 \right)$

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Exam 4: Polynomial and Rational Functions

Use the remainder theorem to find the remainder when f(x)is divided by x - c. - f(x)=x4+8x3+12x2;x+1f ( x ) = x ^ { 4 } + 8 x ^ { 3 } + 12 x ^ { 2 } ; x + 1f(x)=x4+8x3+12x2;x+1

State whether the function is a polynomial function or not. If it is, give its degree. - f(x)=12x4−2x3+2f ( x ) = 12 x ^ { 4 } - 2 x ^ { 3 } + 2f(x)=12x4−2x3+2

Solve the problem. -You have 80 feet of fencing to enclose a rectangular region. What is the maximum area?

Graph the function using transformations. - f(x)=−2x+3f ( x ) = \frac { - 2 } { x + 3 }f(x)=x+3−2​

Use the Factor Theorem to determine whether x - c is a factor of f(x). - f(x)=7x3+26x2−7x−4;x+4f ( x ) = 7 x ^ { 3 } + 26 x ^ { 2 } - 7 x - 4 ; x + 4f(x)=7x3+26x2−7x−4;x+4

For the following rational function, identify the coordinates of all removable discontinuities and sketch the graph. Identify all intercepts and find the equations of all asymptotes. - f(x)=x2−16x−4f ( x ) = \frac { x ^ { 2 } - 16 } { x - 4 }f(x)=x−4x2−16​

State whether the function is a polynomial function or not. If it is, give its degree. -f(x)= 6

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

Graph the function using transformations. - f(x)=5(x+2)2f ( x ) = \frac { 5 } { ( x + 2 ) ^ { 2 } }f(x)=(x+2)25​

Write the equation of the function in the form f(x)= ax2 + bx + c. -

Use the Factor Theorem to determine whether x - c is a factor of f(x). - f(x)=7x3+33x2−9x+5;x+5f ( x ) = 7 x ^ { 3 } + 33 x ^ { 2 } - 9 x + 5 ; x + 5f(x)=7x3+33x2−9x+5;x+5

Use the Factor Theorem to determine whether x - c is a factor of f(x). - f(x)=8x4+23x3−3x2+x+3;x+3f ( x ) = 8 x ^ { 4 } + 23 x ^ { 3 } - 3 x ^ { 2 } + x + 3 ; x + 3f(x)=8x4+23x3−3x2+x+3;x+3

Rewrite the quadratic function in standard form by completing the square. - f(x)=x2−18xf ( x ) = x ^ { 2 } - 18 xf(x)=x2−18x

First rewrite the quadratic function in standard form by completing the square, then find any x-intercepts and any y-intercepts. - f(x)=−9x2−2x−12f ( x ) = - 9 x ^ { 2 } - 2 x - 12f(x)=−9x2−2x−12

Find the coordinates of the vertex of the quadratic function. - f(x)=−4x2−8x−9f ( x ) = - 4 x ^ { 2 } - 8 x - 9f(x)=−4x2−8x−9

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)=x5−3x4−7x3−12x2−13x−7;x−5f ( x ) = x ^ { 5 } - 3 x ^ { 4 } - 7 x ^ { 3 } - 12 x ^ { 2 } - 13 x - 7 ; x - 5f(x)=x5−3x4−7x3−12x2−13x−7;x−5

Sketch the graph of the polynomial function. -

Find the x- and y-intercepts of f. - f(x)=−x2(x+5)(x2−1)f ( x ) = - x ^ { 2 } ( x + 5 ) \left( x ^ { 2 } - 1 \right)f(x)=−x2(x+5)(x2−1)

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

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Use the remainder theorem to find the remainder when f(x)is divided by x - c. - $f ( x ) = x ^ { 4 } + 8 x ^ { 3 } + 12 x ^ { 2 } ; x + 1$

State whether the function is a polynomial function or not. If it is, give its degree. - $f ( x ) = 12 x ^ { 4 } - 2 x ^ { 3 } + 2$

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

Use the Factor Theorem to determine whether x - c is a factor of f(x). - $f ( x ) = 7 x ^ { 3 } + 26 x ^ { 2 } - 7 x - 4 ; x + 4$

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

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

Use the Factor Theorem to determine whether x - c is a factor of f(x). - $f ( x ) = 7 x ^ { 3 } + 33 x ^ { 2 } - 9 x + 5 ; x + 5$

Use the Factor Theorem to determine whether x - c is a factor of f(x). - $f ( x ) = 8 x ^ { 4 } + 23 x ^ { 3 } - 3 x ^ { 2 } + x + 3 ; x + 3$

Rewrite the quadratic function in standard form by completing the square. - $f ( x ) = x ^ { 2 } - 18 x$

First rewrite the quadratic function in standard form by completing the square, then find any x-intercepts and any y-intercepts. - $f ( x ) = - 9 x ^ { 2 } - 2 x - 12$

Find the coordinates of the vertex of the quadratic function. - $f ( x ) = - 4 x ^ { 2 } - 8 x - 9$

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. - $f ( x ) = x ^ { 5 } - 3 x ^ { 4 } - 7 x ^ { 3 } - 12 x ^ { 2 } - 13 x - 7 ; x - 5$

Find the x- and y-intercepts of f. - $f ( x ) = - x ^ { 2 } ( x + 5 ) \left( x ^ { 2 } - 1 \right)$