Question 1

Find the domain and range of the function.
$f ( x ) = 4 x ^ { 2 } - 64 x + 266$

Accepted Answer

A)  $\text { Domain: } ( - \infty , \infty ) \text {; Range: } [ 0 , \infty )$ 
B)  $\text { Domain: } ( - \infty , \infty ) \text {; Range: } ( - \infty , 8 ]$ 
C)  $\text { Domain: } ( - \infty , \infty ) \text {; Range: } [ 10 , \infty )$ 
D)  $\text { Domain: } ( - \infty , \infty ) \text {; Range: } ( - \infty , 0 ]$ 
A)  $\text { Domain: } ( - \infty , \infty ) \text {; Range: } [ 0 , \infty )$ 
B)  $\text { Domain: } ( - \infty , \infty ) \text {; Range: } ( - \infty , 8 ]$ 
C)  $\text { Domain: } ( - \infty , \infty ) \text {; Range: } [ 10 , \infty )$ 
D)  $\text { Domain: } ( - \infty , \infty ) \text {; Range: } ( - \infty , 0 ]$

Question 2

Solve the problem. Round your answer to two decimal places.
-The area of a circle varies directly as the square of the radius of the circle. If a circle with a radius of 5 inches has an area of 78.5 square inches, what is the area of a circle with a radius of 18 inches?

Accepted Answer

A)  $1019.76 \mathrm { in } ^ { 2 }$ 
B)  $1017.36 \mathrm { in } ^ { 2 }$ 
C)  $113.04 \mathrm { in } ^ { 2 }$ 
D)  $56.52 \mathrm { in } ^ { 2 }$ 
A)  $1019.76 \mathrm { in } ^ { 2 }$ 
B)  $1017.36 \mathrm { in } ^ { 2 }$ 
C)  $113.04 \mathrm { in } ^ { 2 }$ 
D)  $56.52 \mathrm { in } ^ { 2 }$

Question 3

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary.
-$$f ( x ) = x ^ { 4 } - 21 x ^ { 2 } - 100$$

Accepted Answer

A)  $- 2 \mathrm { i } , 2 \mathrm { i } , 10 \mathrm { i } , - 10 \mathrm { i }$ 
B)  $- 2 \mathrm { i } , 2 \mathrm { i } , 10 , - 10$ 
C)  $- 2 i , 2 i , 5 i , - 5 i$ 
D)  $- 2 \mathrm { i } , 2 \mathrm { i } , 5 , - 5$ 
A)  $- 2 \mathrm { i } , 2 \mathrm { i } , 10 \mathrm { i } , - 10 \mathrm { i }$ 
B)  $- 2 \mathrm { i } , 2 \mathrm { i } , 10 , - 10$ 
C)  $- 2 i , 2 i , 5 i , - 5 i$ 
D)  $- 2 \mathrm { i } , 2 \mathrm { i } , 5 , - 5$

Question 4

Use the boundedness theorem to determine whether the polynomial function satisfies the given condition.
-The polynomial $f ( x ) = x ^ { 4 } - x ^ { 3 } + 2 x ^ { 2 } - 4 x - 10$ has no real zero less than $- 1$.

Accepted Answer

A)  Yes, the boundedness theorem shows that the polynomial has no real zero less than $- 1$. 
B)  No, the boundedness theorem does not show that the polynomial has no real zero less than $- 1$. 
A)  Yes, the boundedness theorem shows that the polynomial has no real zero less than $- 1$. 
B)  No, the boundedness theorem does not show that the polynomial has no real zero less than $- 1$.

Question 5

Graph the polynomial function. Factor first if the expression is not in factored form.
-$f(x)=(2 x+1)(x-1)(x+2)$

Accepted Answer

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

Question 6

Of all possible pairs of positive numbers having a sum of 72, which pair has the maximum product?

Accepted Answer

A)  27 and 45 
B)  26 and 46 
C)  36 and 36 
D)  35 and 37 
A)  27 and 45 
B)  26 and 46 
C)  36 and 36 
D)  35 and 37

Question 7

Find a polynomial function f(x) of least possible degree having the graph shown.
-

Accepted Answer

A)  $f ( x ) = 4 ( x + 1 ) ^ { 2 } ( x - 1 ) ^ { 2 }$ 
B)  $f ( x ) = - 4 ( x + 1 ) ( x - 1 )$ 
C)  $f ( x ) = 4 ( x + 1 ) ( x - 1 )$ 
D)  $f ( x ) = - 4 ( x + 1 ) ^ { 2 } ( x - 1 ) ^ { 2 }$ 
A)  $f ( x ) = 4 ( x + 1 ) ^ { 2 } ( x - 1 ) ^ { 2 }$ 
B)  $f ( x ) = - 4 ( x + 1 ) ( x - 1 )$ 
C)  $f ( x ) = 4 ( x + 1 ) ( x - 1 )$ 
D)  $f ( x ) = - 4 ( x + 1 ) ^ { 2 } ( x - 1 ) ^ { 2 }$

Question 8

$$\text { How can the graph of } f ( x ) = \frac { 4 } { ( x + 2 ) ^ { 2 } } \text { by obtained from the graph of } y = \frac { 1 } { x ^ { 2 } } ?$$

Accepted Answer

A)  By making a horizontal shift of 2 units to the left and a vertical shift of 4 units down 
B)  By making a horizontal shift of 2 units to the left and stretching vertically by a factor of 4 
C)  By making a horizontal shift of 2 units to the right and stretching vertically by a factor of 4 
D)  By making a horizontal shift of 4 units to the right and a vertical shift of 2 units up 
A)  By making a horizontal shift of 2 units to the left and a vertical shift of 4 units down 
B)  By making a horizontal shift of 2 units to the left and stretching vertically by a factor of 4 
C)  By making a horizontal shift of 2 units to the right and stretching vertically by a factor of 4 
D)  By making a horizontal shift of 4 units to the right and a vertical shift of 2 units up

Question 9

Give the equation of any oblique asymptotes.
-$$h ( x ) = \frac { 5 } { x - 3 }$$

Accepted Answer

A)  $y = 3$ 
B)  $y = x - 3$ 
C)  none 
D)  $x = - 3$ 
A)  $y = 3$ 
B)  $y = x - 3$ 
C)  none 
D)  $x = - 3$

Question 10

Use synthetic division to perform the division.
-$$\frac { x ^ { 3 } - \frac { 5 } { 2 } x ^ { 2 } - 2 x + \frac { 3 } { 2 } } { x - \frac { 1 } { 2 } }$$

Accepted Answer

A)  $x ^ { 2 } + \frac { 13 } { 2 } x + \frac { - 2 } { x + 1 }$ 
B)  $x ^ { 2 } - 2 x - 6$ 
C)  $x ^ { 2 } - 2 x - 3$ 
D)  $x ^ { 2 } + \frac { 13 } { 2 } x + \frac { 7 } { 2 } + 2$ 
A)  $x ^ { 2 } + \frac { 13 } { 2 } x + \frac { - 2 } { x + 1 }$ 
B)  $x ^ { 2 } - 2 x - 6$ 
C)  $x ^ { 2 } - 2 x - 3$ 
D)  $x ^ { 2 } + \frac { 13 } { 2 } x + \frac { 7 } { 2 } + 2$

Question 11

Use synthetic division to decide whether the given number k is a zero of the given polynomial function.
-$k = - 3 ; f ( x ) = x ^ { 4 } - 6 x ^ { 2 } - 27$

Accepted Answer

A) True 
 B)False

Question 12

Find an equation for the rational function graph.
-

Accepted Answer

A)  $f ( x ) = \frac { x ( x - 8 ) } { x - 5 }$ 
B)  $f ( x ) = \frac { x ( x - 8 ) } { ( x - 5 ) ^ { 2 } }$ 
C)  $f ( x ) = \frac { ( x + 8 ) ( x - 8 ) } { x - 5 }$ 
D)  $f ( x ) = \frac { x ( x + 8 ) } { ( x + 5 ) ^ { 2 } }$ 
A)  $f ( x ) = \frac { x ( x - 8 ) } { x - 5 }$ 
B)  $f ( x ) = \frac { x ( x - 8 ) } { ( x - 5 ) ^ { 2 } }$ 
C)  $f ( x ) = \frac { ( x + 8 ) ( x - 8 ) } { x - 5 }$ 
D)  $f ( x ) = \frac { x ( x + 8 ) } { ( x + 5 ) ^ { 2 } }$

Question 13

Sketch the graph of the parabola.
-$$y = \frac { 3 } { 2 } x ^ { 2 } - 4$$

Accepted Answer

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

Question 14

Determine whether the statement is true or false.
-$$\text { The function } f ( x ) = \frac { 3 } { x } \text { is an odd function. }$$

Accepted Answer

A) True 
 B)False

Question 15

If y varies directly as x, and x is doubled, how is y changed?

Accepted Answer

A)  y is halved 
B)  y is increased by 2 
C)  y is unchanged 
D)  y is doubled 
A)  y is halved 
B)  y is increased by 2 
C)  y is unchanged 
D)  y is doubled

Question 16

Use the equation and the corresponding graph for the quadratic function to find what is requested.
-$f(x)=(x-1)^{2}-5$

Find the domain and range.

Accepted Answer

A)  Domain: $[ - 5 , \infty )$; Range: $( -\infty , \infty )$ 
B)  Domain: $( -\infty , \infty )$; Range: $[ - 5 , \infty )$ 
C)  Domain: $( -\infty , \infty )$; Range: $( -\infty , - 5 ]$ 
D)  Domain: $( - 5 , \infty )$; Range: $[ 5 , \infty )$ 
A)  Domain: $[ - 5 , \infty )$; Range: $( -\infty , \infty )$ 
B)  Domain: $( -\infty , \infty )$; Range: $[ - 5 , \infty )$ 
C)  Domain: $( -\infty , \infty )$; Range: $( -\infty , - 5 ]$ 
D)  Domain: $( - 5 , \infty )$; Range: $[ 5 , \infty )$

Question 17

Sketch the graph of the polynomial function.
-

Accepted Answer

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

Question 18

Find the correct end behavior diagram for the given polynomial function.
-$$P ( x ) = 4 - 4 x + x ^ { 2 } - x ^ { 3 } - 4 x ^ { 4 }$$

Accepted Answer

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

Question 19

Determine which of the rational functions given below has the following feature(s).
-There is a "hole" in its graph at $x = 5$

Accepted Answer

A)  $f ( x ) = \frac { x + 9 } { x - 5 }$ 
B)  $f ( x ) = \frac { 5 x - 1 } { x + 9 }$ 
C)  $f ( x ) = \frac { ( x - 5 ) ( x + 9 ) } { ( x + 5 ) ( x - 5 ) }$ 
D)  $f ( x ) = \frac { x + 5 } { ( x + 9 ) ( x + 5 ) }$ 
A)  $f ( x ) = \frac { x + 9 } { x - 5 }$ 
B)  $f ( x ) = \frac { 5 x - 1 } { x + 9 }$ 
C)  $f ( x ) = \frac { ( x - 5 ) ( x + 9 ) } { ( x + 5 ) ( x - 5 ) }$ 
D)  $f ( x ) = \frac { x + 5 } { ( x + 9 ) ( x + 5 ) }$

Question 20

Graph the polynomial function. Factor first if the expression is not in factored form.
-

Accepted Answer

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

Find the domain and range of the function. $f ( x ) = 4 x ^ { 2 } - 64 x + 266$

Solve the problem. Round your answer to two decimal places. -The area of a circle varies directly as the square of the radius of the circle. If a circle with a radius of 5 inches has an area of 78.5 square inches, what is the area of a circle with a radius of 18 inches?

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 4 } - 21 x ^ { 2 } - 100$

Use the boundedness theorem to determine whether the polynomial function satisfies the given condition. -The polynomial $f ( x ) = x ^ { 4 } - x ^ { 3 } + 2 x ^ { 2 } - 4 x - 10$ has no real zero less than $- 1$ .

Graph the polynomial function. Factor first if the expression is not in factored form. - $f(x)=(2 x+1)(x-1)(x+2)$

Of all possible pairs of positive numbers having a sum of 72, which pair has the maximum product?

Find a polynomial function f(x) of least possible degree having the graph shown. -

$\text { How can the graph of } f ( x ) = \frac { 4 } { ( x + 2 ) ^ { 2 } } \text { by obtained from the graph of } y = \frac { 1 } { x ^ { 2 } } ?$

Give the equation of any oblique asymptotes. - $h ( x ) = \frac { 5 } { x - 3 }$

Use synthetic division to perform the division. - $\frac { x ^ { 3 } - \frac { 5 } { 2 } x ^ { 2 } - 2 x + \frac { 3 } { 2 } } { x - \frac { 1 } { 2 } }$

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $k = - 3 ; f ( x ) = x ^ { 4 } - 6 x ^ { 2 } - 27$

Find an equation for the rational function graph. -

Sketch the graph of the parabola. - $y = \frac { 3 } { 2 } x ^ { 2 } - 4$ $Sketch the graph of the parabola. - y = \frac { 3 } { 2 } x ^ { 2 } - 4$

Determine whether the statement is true or false. - $\text { The function } f ( x ) = \frac { 3 } { x } \text { is an odd function. }$

If y varies directly as x, and x is doubled, how is y changed?

Use the equation and the corresponding graph for the quadratic function to find what is requested. - $f(x)=(x-1)^{2}-5$ $Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=(x-1)^{2}-5 Find the domain and range.$ Find the domain and range.

Sketch the graph of the polynomial function. -

Find the correct end behavior diagram for the given polynomial function. - $P ( x ) = 4 - 4 x + x ^ { 2 } - x ^ { 3 } - 4 x ^ { 4 }$

Determine which of the rational functions given below has the following feature(s). -There is a "hole" in its graph at $x = 5$

Graph the polynomial function. Factor first if the expression is not in factored form. -

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 4: Polynomials and Rational Functions

Find the domain and range of the function. f(x)=4x2−64x+266f ( x ) = 4 x ^ { 2 } - 64 x + 266f(x)=4x2−64x+266

Solve the problem. Round your answer to two decimal places. -The area of a circle varies directly as the square of the radius of the circle. If a circle with a radius of 5 inches has an area of 78.5 square inches, what is the area of a circle with a radius of 18 inches?

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - f(x)=x4−21x2−100f ( x ) = x ^ { 4 } - 21 x ^ { 2 } - 100f(x)=x4−21x2−100

Use the boundedness theorem to determine whether the polynomial function satisfies the given condition. -The polynomial f(x)=x4−x3+2x2−4x−10f ( x ) = x ^ { 4 } - x ^ { 3 } + 2 x ^ { 2 } - 4 x - 10f(x)=x4−x3+2x2−4x−10 has no real zero less than −1- 1−1 .

Graph the polynomial function. Factor first if the expression is not in factored form. - f(x)=(2x+1)(x−1)(x+2)f(x)=(2 x+1)(x-1)(x+2)f(x)=(2x+1)(x−1)(x+2)

Of all possible pairs of positive numbers having a sum of 72, which pair has the maximum product?

Find a polynomial function f(x) of least possible degree having the graph shown. -

How can the graph of f(x)=4(x+2)2 by obtained from the graph of y=1x2?\text { How can the graph of } f ( x ) = \frac { 4 } { ( x + 2 ) ^ { 2 } } \text { by obtained from the graph of } y = \frac { 1 } { x ^ { 2 } } ? How can the graph of f(x)=(x+2)24​ by obtained from the graph of y=x21​?

Give the equation of any oblique asymptotes. - h(x)=5x−3h ( x ) = \frac { 5 } { x - 3 }h(x)=x−35​

Use synthetic division to perform the division. - x3−52x2−2x+32x−12\frac { x ^ { 3 } - \frac { 5 } { 2 } x ^ { 2 } - 2 x + \frac { 3 } { 2 } } { x - \frac { 1 } { 2 } }x−21​x3−25​x2−2x+23​​

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - k=−3;f(x)=x4−6x2−27k = - 3 ; f ( x ) = x ^ { 4 } - 6 x ^ { 2 } - 27k=−3;f(x)=x4−6x2−27

Find an equation for the rational function graph. -

Sketch the graph of the parabola. - y=32x2−4y = \frac { 3 } { 2 } x ^ { 2 } - 4y=23​x2−4

Determine whether the statement is true or false. - The function f(x)=3x is an odd function. \text { The function } f ( x ) = \frac { 3 } { x } \text { is an odd function. } The function f(x)=x3​ is an odd function.

If y varies directly as x, and x is doubled, how is y changed?

Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=(x−1)2−5f(x)=(x-1)^{2}-5f(x)=(x−1)2−5 Find the domain and range.

Sketch the graph of the polynomial function. -

Find the correct end behavior diagram for the given polynomial function. - P(x)=4−4x+x2−x3−4x4P ( x ) = 4 - 4 x + x ^ { 2 } - x ^ { 3 } - 4 x ^ { 4 }P(x)=4−4x+x2−x3−4x4

Determine which of the rational functions given below has the following feature(s). -There is a "hole" in its graph at x=5x = 5x=5

Graph the polynomial function. Factor first if the expression is not in factored form. -

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Find the domain and range of the function. $f ( x ) = 4 x ^ { 2 } - 64 x + 266$

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 4 } - 21 x ^ { 2 } - 100$

Use the boundedness theorem to determine whether the polynomial function satisfies the given condition. -The polynomial $f ( x ) = x ^ { 4 } - x ^ { 3 } + 2 x ^ { 2 } - 4 x - 10$ has no real zero less than $- 1$ .

Graph the polynomial function. Factor first if the expression is not in factored form. - $f(x)=(2 x+1)(x-1)(x+2)$

$\text { How can the graph of } f ( x ) = \frac { 4 } { ( x + 2 ) ^ { 2 } } \text { by obtained from the graph of } y = \frac { 1 } { x ^ { 2 } } ?$

Give the equation of any oblique asymptotes. - $h ( x ) = \frac { 5 } { x - 3 }$

Use synthetic division to perform the division. - $\frac { x ^ { 3 } - \frac { 5 } { 2 } x ^ { 2 } - 2 x + \frac { 3 } { 2 } } { x - \frac { 1 } { 2 } }$

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $k = - 3 ; f ( x ) = x ^ { 4 } - 6 x ^ { 2 } - 27$

Sketch the graph of the parabola. - $y = \frac { 3 } { 2 } x ^ { 2 } - 4$ $Sketch the graph of the parabola. - y = \frac { 3 } { 2 } x ^ { 2 } - 4$

Determine whether the statement is true or false. - $\text { The function } f ( x ) = \frac { 3 } { x } \text { is an odd function. }$

Use the equation and the corresponding graph for the quadratic function to find what is requested. - $f(x)=(x-1)^{2}-5$ $Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=(x-1)^{2}-5 Find the domain and range.$ Find the domain and range.

Find the correct end behavior diagram for the given polynomial function. - $P ( x ) = 4 - 4 x + x ^ { 2 } - x ^ { 3 } - 4 x ^ { 4 }$

Determine which of the rational functions given below has the following feature(s). -There is a "hole" in its graph at $x = 5$