Question 1

Find the domain and range of the function.
$y = ( x - 9 ) ^ { 2 } + 6$

Accepted Answer

A)  $\text { Domain: } [ 9 , \infty ) \text {; Range: } [ - \infty , - 9 )$ 
B)  $\text { Domain: } ( - \infty , \infty ) \text {; Range: } [ 6 , \infty )$ 
C)  $\text { Domain: } ( - \infty , \infty ) \text {; Range: } [ 9 , \infty )$ 
D)  $\text { Domain: } [ 6 , \infty ) \text {; Range: } [ - \infty , 6 )$ 
A)  $\text { Domain: } [ 9 , \infty ) \text {; Range: } [ - \infty , - 9 )$ 
B)  $\text { Domain: } ( - \infty , \infty ) \text {; Range: } [ 6 , \infty )$ 
C)  $\text { Domain: } ( - \infty , \infty ) \text {; Range: } [ 9 , \infty )$ 
D)  $\text { Domain: } [ 6 , \infty ) \text {; Range: } [ - \infty , 6 )$

Question 2

Give the equations of any horizontal asymptotes.
-$$f ( x ) = \frac { x ^ { 2 } + 9 } { x ^ { 2 } - 9 }$$

Accepted Answer

A)  $y = 0$ 
B)  $y = 9$ 
C)  none 
D)  $y = 1$ 
A)  $y = 0$ 
B)  $y = 9$ 
C)  none 
D)  $y = 1$

Question 3

Sketch the graph of the parabola.
-$$y = - x ^ { 2 } + 2 x - 6$$

Accepted Answer

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

Question 4

Find the correct end behavior diagram for the given polynomial function.
-$$P ( x ) = 3 x ^ { 7 } + 6 x ^ { 2 } - 6$$

Accepted Answer

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

Question 5

Find the equation that the given graph represents.
-

Accepted Answer

A)  $P ( x ) = x ^ { 6 } - 2 x ^ { 2 } - 6$ 
B)  $P ( x ) = - x ^ { 5 } - 3 x ^ { 2 } + 6$ 
C)  $P ( x ) = x ^ { 5 } + 2 x ^ { 3 } + 6$ 
D)  $P ( x ) = x ^ { 4 } - 3 x ^ { 2 } + 6$ 
A)  $P ( x ) = x ^ { 6 } - 2 x ^ { 2 } - 6$ 
B)  $P ( x ) = - x ^ { 5 } - 3 x ^ { 2 } + 6$ 
C)  $P ( x ) = x ^ { 5 } + 2 x ^ { 3 } + 6$ 
D)  $P ( x ) = x ^ { 4 } - 3 x ^ { 2 } + 6$

Question 6

Tell whether a linear model or a quadratic model is appropriate for the data. If linear, tell whether the slope should be positive or negative. If quadratic, decide whether the leading coefficient a of $x ^ { 2 }$ should be positive or negative.
-The height of a ball thrown from the ground, as a function of time.

Accepted Answer

A)  linear; positive 
B)  linear; negative 
C)  quadratic; positive 
D)  quadratic; negative 
A)  linear; positive 
B)  linear; negative 
C)  quadratic; positive 
D)  quadratic; negative

Question 7

Give the equations of any horizontal asymptotes.
-$$h ( x ) = \frac { 3 - 8 x } { - 6 x + 9 }$$

Accepted Answer

A)  $y = 0$ 
B)  none 
C)  $y = \frac { 4 } { 3 }$ 
D)  $y = - \frac { 4 } { 3 }$ 
A)  $y = 0$ 
B)  none 
C)  $y = \frac { 4 } { 3 }$ 
D)  $y = - \frac { 4 } { 3 }$

Question 8

Find an equation for the rational function graph.
-

Accepted Answer

A)  $f ( x ) = \frac { x + 4 } { x - 4 }$ 
B)  $f ( x ) = \frac { ( x - 4 ) ( x + 6 ) } { ( x + 4 ) ( x + 6 ) }$ 
C)  $f ( x ) = \frac { ( x + 4 ) ( x - 6 ) } { ( x - 4 ) ( x - 6 ) }$ 
D)  $f ( x ) = \frac { ( x - 4 ) ( x - 6 ) } { ( x + 4 ) ( x - 6 ) }$ 
A)  $f ( x ) = \frac { x + 4 } { x - 4 }$ 
B)  $f ( x ) = \frac { ( x - 4 ) ( x + 6 ) } { ( x + 4 ) ( x + 6 ) }$ 
C)  $f ( x ) = \frac { ( x + 4 ) ( x - 6 ) } { ( x - 4 ) ( x - 6 ) }$ 
D)  $f ( x ) = \frac { ( x - 4 ) ( x - 6 ) } { ( x + 4 ) ( x - 6 ) }$

Question 9

Sketch the graph of the rational function.
-$$f ( x ) = \frac { x ^ { 2 } + 6 x - 7 } { x ^ { 2 } - x - 12 }$$

Accepted Answer

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

Question 10

Match the equation to the correct graph.
$y = - \frac { 1 } { 2 } ( x + 4 ) ^ { 2 } - 1$

Accepted Answer

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

Question 11

A biking club has increased its membership each year since its founding in 1984. The table provides membership data for several years.

Determine the linear, quadratic, cubic, or quartic function that best fits the data.

Accepted Answer

A)  $f ( x ) = 0.0002 x ^ { 3 } - 0.006 x ^ { 2 } + 0.99 x + 7.03$ 
B)  $f ( x ) = 0.94 x + 7.08$ 
C)  $f ( x ) = - 0.003 x ^ { 2 } + 0.98 x + 7.03$ 
D)  $f ( x ) = 0.003 x ^ { 4 } - 0.98 x ^ { 2 } + 7.03 x + 1.57$ 
A)  $f ( x ) = 0.0002 x ^ { 3 } - 0.006 x ^ { 2 } + 0.99 x + 7.03$ 
B)  $f ( x ) = 0.94 x + 7.08$ 
C)  $f ( x ) = - 0.003 x ^ { 2 } + 0.98 x + 7.03$ 
D)  $f ( x ) = 0.003 x ^ { 4 } - 0.98 x ^ { 2 } + 7.03 x + 1.57$

Question 12

Round to the nearest tenth unless indicated otherwise.
-The force needed to keep a car from skidding on a curve varies jointly as the weight of the car and the square of the car's speed, and inversely as the radius of the curve. If a force of 3600 pounds is needed to keep an
1800 pound car traveling at 20 mph from skidding on a curve of radius 600 feet, what force would be required
To keep the same car from skidding on a curve of radius 640 feet at 50 mph? Round your answer to the nearest
Pound of force.

Accepted Answer

A)  20,962 lb 
B)  21,094 lb 
C)  21,126 lb 
D)  21,664 lb 
A)  20,962 lb 
B)  21,094 lb 
C)  21,126 lb 
D)  21,664 lb

Question 13

Provide an appropriate response.
-How many real zeros does this graph have?

Accepted Answer

A)  2 
B)  1 
C)  4 
D)  3 
A)  2 
B)  1 
C)  4 
D)  3

Question 14

Use synthetic division $$f ( x ) \text { by } x - k \text { for the given value of } k \text {. Then express } f ( x ) \text { in the form } f ( x ) = ( x - k ) q ( x ) + r$$ for the given value of k.
-$$f ( x ) = 3 x ^ { 4 } - 9 x ^ { 3 } + 2 x ^ { 2 } - 6 x ; \quad k = 3$$

Accepted Answer

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

Question 15

Graph the polynomial function. Factor first if the expression is not in factored form.
-$f(x)=x(x+1)(x-2)^{3}$

Accepted Answer

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

Question 16

Given the equation or other information for a parabola, find the matching description or graph.
$\begin{array} { l } 
f ( x ) = a x ^ { 2 } + b x + c \
a < 0 ; b ^ { 2 } - 4 a c < 0
\end{array}$

Accepted Answer

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

Question 17

Determine whether the statement is true or false.
-$$\text { If } \mathrm { f } ( \mathrm { x } ) \text { is a polynomial having only real coefficients and } 1 - 4 i \text { is a zero of } \mathrm { f } ( \mathrm { x } ) \text {, then } - 1 + 4 \mathrm { i } \text { is also a zero. }$$

Accepted Answer

A) True 
 B)False

Question 18

Solve the inequality. Write the solution set in interval notation.
-$$- x ^ { 2 } + 10 x - 23 < 0$$

Accepted Answer

A)  $( - 5 - \sqrt { 2 } , - 5 + \sqrt { 2 } )$ 
B)  $( 5 - \sqrt { 2 } , 5 + \sqrt { 2 } )$ 
C)  $( -\infty , 5 - \sqrt { 2 } ) \cup ( 5 + \sqrt { 2 } , \infty )$ 
D)  $( -\infty , - 5 - \sqrt { 2 } ) \cup ( - 5 + \sqrt { 2 } , \infty )$ 
A)  $( - 5 - \sqrt { 2 } , - 5 + \sqrt { 2 } )$ 
B)  $( 5 - \sqrt { 2 } , 5 + \sqrt { 2 } )$ 
C)  $( -\infty , 5 - \sqrt { 2 } ) \cup ( 5 + \sqrt { 2 } , \infty )$ 
D)  $( -\infty , - 5 - \sqrt { 2 } ) \cup ( - 5 + \sqrt { 2 } , \infty )$

Question 19

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given.
-$f ( x ) = 2 x ^ { 3 } - 7 x ^ { 2 } + 4 x + 8 ; - 1$ and 0

Accepted Answer

A)  $f ( - 1 ) = 5$ and $f ( 0 ) = - 8$ 
B)  $f ( - 1 ) = - 4$ and $f ( 0 ) = 9$ 
C)  $f ( - 1 ) = - 5$ and $f ( 0 ) = 8$ 
D)  $f ( - 1 ) = 5$ and $f ( 0 ) = 8$ 
A)  $f ( - 1 ) = 5$ and $f ( 0 ) = - 8$ 
B)  $f ( - 1 ) = - 4$ and $f ( 0 ) = 9$ 
C)  $f ( - 1 ) = - 5$ and $f ( 0 ) = 8$ 
D)  $f ( - 1 ) = 5$ and $f ( 0 ) = 8$

Question 20

A quadratic equation f(x)=0  has a solution  x=3 . Its graph has vertex  (-1,-16) . What is the other solution of the equation?

Accepted Answer

A)  7 
B)   -4 
C)   -3 
D)   -5 
A)  7 
B)   -4 
C)   -3 
D)   -5

Find the domain and range of the function. $y = ( x - 9 ) ^ { 2 } + 6$

Give the equations of any horizontal asymptotes. - $f ( x ) = \frac { x ^ { 2 } + 9 } { x ^ { 2 } - 9 }$

Sketch the graph of the parabola. - $y = - x ^ { 2 } + 2 x - 6$ $Sketch the graph of the parabola. - y = - x ^ { 2 } + 2 x - 6$

Find the correct end behavior diagram for the given polynomial function. - $P ( x ) = 3 x ^ { 7 } + 6 x ^ { 2 } - 6$

Find the equation that the given graph represents. -

Give the equations of any horizontal asymptotes. - $h ( x ) = \frac { 3 - 8 x } { - 6 x + 9 }$

Find an equation for the rational function graph. -

Sketch the graph of the rational function. - $f ( x ) = \frac { x ^ { 2 } + 6 x - 7 } { x ^ { 2 } - x - 12 }$ $Sketch the graph of the rational function. - f ( x ) = \frac { x ^ { 2 } + 6 x - 7 } { x ^ { 2 } - x - 12 }$

Match the equation to the correct graph. $y = - \frac { 1 } { 2 } ( x + 4 ) ^ { 2 } - 1$

A biking club has increased its membership each year since its founding in 1984. The table provides membership data for several years. Determine the linear, quadratic, cubic, or quartic function that best fits the data.

Provide an appropriate response. -How many real zeros does this graph have?

Use synthetic division $f ( x ) \text { by } x - k \text { for the given value of } k \text {. Then express } f ( x ) \text { in the form } f ( x ) = ( x - k ) q ( x ) + r$ for the given value of k. - $f ( x ) = 3 x ^ { 4 } - 9 x ^ { 3 } + 2 x ^ { 2 } - 6 x ; \quad k = 3$

Graph the polynomial function. Factor first if the expression is not in factored form. - $f(x)=x(x+1)(x-2)^{3}$ $Graph the polynomial function. Factor first if the expression is not in factored form. - f(x)=x(x+1)(x-2)^{3}$

Given the equation or other information for a parabola, find the matching description or graph. f(x)=a+bx+c a<0;-4ac<0

Determine whether the statement is true or false. - $\text { If } \mathrm { f } ( \mathrm { x } ) \text { is a polynomial having only real coefficients and } 1 - 4 i \text { is a zero of } \mathrm { f } ( \mathrm { x } ) \text {, then } - 1 + 4 \mathrm { i } \text { is also a zero. }$

Solve the inequality. Write the solution set in interval notation. - $- x ^ { 2 } + 10 x - 23 < 0$

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given. - $f ( x ) = 2 x ^ { 3 } - 7 x ^ { 2 } + 4 x + 8 ; - 1$ and 0

A quadratic equation f(x)=0 has a solution x=3 . Its graph has vertex (-1,-16) . What is the other solution of the equation?

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. y=(x−9)2+6y = ( x - 9 ) ^ { 2 } + 6y=(x−9)2+6

Give the equations of any horizontal asymptotes. - f(x)=x2+9x2−9f ( x ) = \frac { x ^ { 2 } + 9 } { x ^ { 2 } - 9 }f(x)=x2−9x2+9​

Sketch the graph of the parabola. - y=−x2+2x−6y = - x ^ { 2 } + 2 x - 6y=−x2+2x−6

Find the correct end behavior diagram for the given polynomial function. - P(x)=3x7+6x2−6P ( x ) = 3 x ^ { 7 } + 6 x ^ { 2 } - 6P(x)=3x7+6x2−6

Find the equation that the given graph represents. -

Give the equations of any horizontal asymptotes. - h(x)=3−8x−6x+9h ( x ) = \frac { 3 - 8 x } { - 6 x + 9 }h(x)=−6x+93−8x​

Find an equation for the rational function graph. -

Sketch the graph of the rational function. - f(x)=x2+6x−7x2−x−12f ( x ) = \frac { x ^ { 2 } + 6 x - 7 } { x ^ { 2 } - x - 12 }f(x)=x2−x−12x2+6x−7​

Match the equation to the correct graph. y=−12(x+4)2−1y = - \frac { 1 } { 2 } ( x + 4 ) ^ { 2 } - 1y=−21​(x+4)2−1

A biking club has increased its membership each year since its founding in 1984. The table provides membership data for several years. Determine the linear, quadratic, cubic, or quartic function that best fits the data.

Provide an appropriate response. -How many real zeros does this graph have?

Graph the polynomial function. Factor first if the expression is not in factored form. - f(x)=x(x+1)(x−2)3f(x)=x(x+1)(x-2)^{3}f(x)=x(x+1)(x−2)3

Given the equation or other information for a parabola, find the matching description or graph. f(x)=a+bx+c a<0;-4ac<0

Solve the inequality. Write the solution set in interval notation. - −x2+10x−23<0- x ^ { 2 } + 10 x - 23 < 0−x2+10x−23<0

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given. - f(x)=2x3−7x2+4x+8;−1f ( x ) = 2 x ^ { 3 } - 7 x ^ { 2 } + 4 x + 8 ; - 1f(x)=2x3−7x2+4x+8;−1 and 0

A quadratic equation f(x)=0 has a solution x=3 . Its graph has vertex (-1,-16) . What is the other solution of the equation?

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. $y = ( x - 9 ) ^ { 2 } + 6$

Give the equations of any horizontal asymptotes. - $f ( x ) = \frac { x ^ { 2 } + 9 } { x ^ { 2 } - 9 }$

Sketch the graph of the parabola. - $y = - x ^ { 2 } + 2 x - 6$ $Sketch the graph of the parabola. - y = - x ^ { 2 } + 2 x - 6$

Find the correct end behavior diagram for the given polynomial function. - $P ( x ) = 3 x ^ { 7 } + 6 x ^ { 2 } - 6$

Give the equations of any horizontal asymptotes. - $h ( x ) = \frac { 3 - 8 x } { - 6 x + 9 }$

Sketch the graph of the rational function. - $f ( x ) = \frac { x ^ { 2 } + 6 x - 7 } { x ^ { 2 } - x - 12 }$ $Sketch the graph of the rational function. - f ( x ) = \frac { x ^ { 2 } + 6 x - 7 } { x ^ { 2 } - x - 12 }$

Match the equation to the correct graph. $y = - \frac { 1 } { 2 } ( x + 4 ) ^ { 2 } - 1$

Graph the polynomial function. Factor first if the expression is not in factored form. - $f(x)=x(x+1)(x-2)^{3}$ $Graph the polynomial function. Factor first if the expression is not in factored form. - f(x)=x(x+1)(x-2)^{3}$

Solve the inequality. Write the solution set in interval notation. - $- x ^ { 2 } + 10 x - 23 < 0$

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given. - $f ( x ) = 2 x ^ { 3 } - 7 x ^ { 2 } + 4 x + 8 ; - 1$ and 0