Question 1

Determine the maximum possible number of turning points for the graph of the function.
-$$f ( x ) = ( 2 x + 3 ) ^ { 2 } \left( x ^ { 2 } - 1 \right) ( x + 1 )$$

Accepted Answer

A)  10 
B)  4 
C)  5 
D)  2 
A)  10 
B)  4 
C)  5 
D)  2

Question 2

The graph of a quadratic function is given. Determine the function's equation.
-

Accepted Answer

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

Question 3

Write the equation of a polynomial function with the given characteristics. Use a leading coefficient of 1 or -1 and make
the degree of the function as small as possible.
-Touches the $x$-axis at 0 and crosses the $x$-axis at 4 ; lies above the $x$-axis between 0 and 4 .

Accepted Answer

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

Question 4

Use the vertex and intercepts to sketch the graph of the quadratic function.
-$f ( x ) = - x ^ { 2 } + 4 x + 5$

Accepted Answer

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

Question 5

Find the coordinates of the vertex for the parabola defined by the given quadratic function.
-$$f ( x ) = 3 x ^ { 2 } - 6 x - 5$$

Accepted Answer

A)  $( 1 , - 8 )$ 
B)  $( - 1,4 )$ 
C)  $( - 2,19 )$ 
D)  $( 2,1 )$ 
A)  $( 1 , - 8 )$ 
B)  $( - 1,4 )$ 
C)  $( - 2,19 )$ 
D)  $( 2,1 )$

Question 6

Find the degree of the polynomial function.
-$$g ( x ) = 10 x ^ { 4 } + 2$$

Accepted Answer

A)  10 
B)  0 
C)  4 
D)  5 
A)  10 
B)  0 
C)  4 
D)  5

Question 7

Solve the problem
-The following table shows the number of fires in a county for the years 1994-1998, where 1 represents 1994, 2 represents 1995, and so on.
 
This data can be approximated using the third-degree polynomial
$T ( x ) = - 0.49 x ^ { 3 } + 0.57 x ^ { 2 } + 65.40 x + 2655.2$
Use this function to predict the number of fires in 2004. Round to the nearest whole number.

Accepted Answer

A)  2072 
B)  2777 
C)  2791 
D)  148 
A)  2072 
B)  2777 
C)  2791 
D)  148

Question 8

Find the coordinates of the vertex for the parabola defined by the given quadratic function.
-$$y + 4 = ( x + 2 ) ^ { 2 }$$

Accepted Answer

A)  $( - 2 , - 4 )$ 
B)  $( 4,2 )$ 
C)  $( 2 , - 4 )$ 
D)  $( 4 , - 2 )$ 
A)  $( - 2 , - 4 )$ 
B)  $( 4,2 )$ 
C)  $( 2 , - 4 )$ 
D)  $( 4 , - 2 )$

Question 9

Find the y-intercept for the graph of the quadratic function.
-$$y + 9 = ( x + 3 ) ^ { 2 }$$

Accepted Answer

A)  $( 0,0 )$ 
B)  $( 9,0 )$ 
C)  $( 0,6 )$ 
D)  $( 0 , - 6 )$ 
A)  $( 0,0 )$ 
B)  $( 9,0 )$ 
C)  $( 0,6 )$ 
D)  $( 0 , - 6 )$

Question 10

Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and
turns around, at each intercept.
-$$f ( x ) = - x ^ { 3 } ( x + 3 ) ^ { 2 } ( x - 8 )$$

Accepted Answer

A)  0 , crosses the $x$-axis;
$- 3$, touches the $x$-axis and turns around;
8 , crosses the $x$-axis 
B)  0 , touches the $x$-axis and turns around;
3 , crosses the $x$-axis;
8 , crosses the $x$-axis 
C)  0 , crosses the x-axis;
3 , touches the $x$-axis and turns around;
$- 8$, crosses the $x$-axis 
D)  0 , touches the $x$-axis and turns around;
$- 3$, touches the $x$-axis and turns around;
8 , crosses the $\mathrm { x }$-axis 
A)  0 , crosses the $x$-axis;
$- 3$, touches the $x$-axis and turns around;
8 , crosses the $x$-axis 
B)  0 , touches the $x$-axis and turns around;
3 , crosses the $x$-axis;
8 , crosses the $x$-axis 
C)  0 , crosses the x-axis;
3 , touches the $x$-axis and turns around;
$- 8$, crosses the $x$-axis 
D)  0 , touches the $x$-axis and turns around;
$- 3$, touches the $x$-axis and turns around;
8 , crosses the $\mathrm { x }$-axis

Question 11

Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither.
-$$f ( x ) = ( x + 1 ) ( x - 2 ) ( x - 1 ) ^ { 2 }$$

Accepted Answer

A)  $y$-axis symmetry 
B)  origin symmetry 
C)  neither 
A)  $y$-axis symmetry 
B)  origin symmetry 
C)  neither

Question 12

Find the coordinates of the vertex for the parabola defined by the given quadratic function.
-$$f ( x ) = x ^ { 2 } + 6$$

Accepted Answer

A)  $( 0,6 )$ 
B)  $( 0 , - 6 )$ 
C)  $( 6,0 )$ 
D)  $( - 6,0 )$ 
A)  $( 0,6 )$ 
B)  $( 0 , - 6 )$ 
C)  $( 6,0 )$ 
D)  $( - 6,0 )$

Question 13

Find the domain and range of the quadratic function whose graph is described.
-The maximum is $- 6$ at $x = - 1$

Accepted Answer

A)  Domain: $( - \infty , \infty )$
Range: $( - \infty , - 1 ]$ 
B)  Domain: $( - \infty , \infty )$
Range: $[ - 6 , \infty )$ 
C)  Domain: $( - \infty , - 1 ]$
Range: $( - \infty , - 6 ]$ 
D)  Domain: $( - \infty , \infty )$
Range: $( - \infty , - 6 ]$ 
A)  Domain: $( - \infty , \infty )$
Range: $( - \infty , - 1 ]$ 
B)  Domain: $( - \infty , \infty )$
Range: $[ - 6 , \infty )$ 
C)  Domain: $( - \infty , - 1 ]$
Range: $( - \infty , - 6 ]$ 
D)  Domain: $( - \infty , \infty )$
Range: $( - \infty , - 6 ]$

Question 14

Use the Leading Coefficient Test to determine the end behavior of the polynomial function.
-$$f ( x ) = x ^ { 3 } - 4 x ^ { 2 } + 2 x + 3$$

Accepted Answer

A)  falls to the left and falls to the right 
B)  rises to the left and falls to the right 
C)  rises to the left and rises to the right 
D)  falls to the left and rises to the right 
A)  falls to the left and falls to the right 
B)  rises to the left and falls to the right 
C)  rises to the left and rises to the right 
D)  falls to the left and rises to the right

Question 15

Find the y-intercept for the graph of the quadratic function.
-$$f ( x ) = 4 x ^ { 2 } - 3 x - 7$$

Accepted Answer

A)  $( 0 , - 7 )$ 
B)  $\left( 0 , \frac { 7 } { 4 } \right)$ 
C)  $\left( 0 , - \frac { 7 } { 4 } \right)$ 
D)  $( 0,7 )$ 
A)  $( 0 , - 7 )$ 
B)  $\left( 0 , \frac { 7 } { 4 } \right)$ 
C)  $\left( 0 , - \frac { 7 } { 4 } \right)$ 
D)  $( 0,7 )$

Question 16

Determine whether the function is a polynomial function.
-$$f ( x ) = \pi x ^ { 3 } - 2 x ^ { 2 } - 1$$

Accepted Answer

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

Question 17

Determine the maximum possible number of turning points for the graph of the function.
-$$y ( x ) = 4 x + 4$$

Accepted Answer

A)  3 
B)  2 
C)  1 
D)  0 
A)  3 
B)  2 
C)  1 
D)  0

Question 18

Solve the problem
-The manufacturer of a CD player has found that the revenue $R$ (in dollars) is $R ( p ) = - 4 p ^ { 2 } + 1560 p$, when the unit price is $p$ dollars. If the manufacturer sets the price $p$ to maximize revenue, what is the maximum revenue to the nearest whole dollar?

Accepted Answer

A)  $\$ 152,100$ 
B)  $\$ 608,400$ 
C)  $\$ 1,216,800$ 
D)  $\$ 304,200$ 
A)  $\$ 152,100$ 
B)  $\$ 608,400$ 
C)  $\$ 1,216,800$ 
D)  $\$ 304,200$

Question 19

Use the vertex and intercepts to sketch the graph of the quadratic function.
-$f ( x ) = 4 - ( x - 2 ) ^ { 2 }$

Accepted Answer

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

Question 20

Use the Leading Coefficient Test to determine the end behavior of the polynomial function.
-$$f ( x ) = ( x - 1 ) ( x + 1 ) ( x + 3 ) ^ { 3 }$$

Accepted Answer

A)  rises to the left and rises to the right 
B)  falls to the left and falls to the right 
C)  rises to the left and falls to the right 
D)  falls to the left and rises to the right 
A)  rises to the left and rises to the right 
B)  falls to the left and falls to the right 
C)  rises to the left and falls to the right 
D)  falls to the left and rises to the right

Determine the maximum possible number of turning points for the graph of the function. - $f ( x ) = ( 2 x + 3 ) ^ { 2 } \left( x ^ { 2 } - 1 \right) ( x + 1 )$

The graph of a quadratic function is given. Determine the function's equation. -

Write the equation of a polynomial function with the given characteristics. Use a leading coefficient of 1 or -1 and make the degree of the function as small as possible. -Touches the $x$ -axis at 0 and crosses the $x$ -axis at 4 ; lies above the $x$ -axis between 0 and 4 .

Use the vertex and intercepts to sketch the graph of the quadratic function. - $f ( x ) = - x ^ { 2 } + 4 x + 5$ $Use the vertex and intercepts to sketch the graph of the quadratic function. - f ( x ) = - x ^ { 2 } + 4 x + 5$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = 3 x ^ { 2 } - 6 x - 5$

Find the degree of the polynomial function. - $g ( x ) = 10 x ^ { 4 } + 2$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $y + 4 = ( x + 2 ) ^ { 2 }$

Find the y-intercept for the graph of the quadratic function. - $y + 9 = ( x + 3 ) ^ { 2 }$

Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. - $f ( x ) = - x ^ { 3 } ( x + 3 ) ^ { 2 } ( x - 8 )$

Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. - $f ( x ) = ( x + 1 ) ( x - 2 ) ( x - 1 ) ^ { 2 }$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = x ^ { 2 } + 6$

Find the domain and range of the quadratic function whose graph is described. -The maximum is $- 6$ at $x = - 1$

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. - $f ( x ) = x ^ { 3 } - 4 x ^ { 2 } + 2 x + 3$

Find the y-intercept for the graph of the quadratic function. - $f ( x ) = 4 x ^ { 2 } - 3 x - 7$

Determine whether the function is a polynomial function. - $f ( x ) = \pi x ^ { 3 } - 2 x ^ { 2 } - 1$

Determine the maximum possible number of turning points for the graph of the function. - $y ( x ) = 4 x + 4$

Solve the problem -The manufacturer of a CD player has found that the revenue $R$ (in dollars) is $R ( p ) = - 4 p ^ { 2 } + 1560 p$ , when the unit price is $p$ dollars. If the manufacturer sets the price $p$ to maximize revenue, what is the maximum revenue to the nearest whole dollar?

Use the vertex and intercepts to sketch the graph of the quadratic function. - $f ( x ) = 4 - ( x - 2 ) ^ { 2 }$ $Use the vertex and intercepts to sketch the graph of the quadratic function. - f ( x ) = 4 - ( x - 2 ) ^ { 2 }$

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. - $f ( x ) = ( x - 1 ) ( x + 1 ) ( x + 3 ) ^ { 3 }$

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Exam 3: Polynomial and Rational Functions

Determine the maximum possible number of turning points for the graph of the function. - f(x)=(2x+3)2(x2−1)(x+1)f ( x ) = ( 2 x + 3 ) ^ { 2 } \left( x ^ { 2 } - 1 \right) ( x + 1 )f(x)=(2x+3)2(x2−1)(x+1)

The graph of a quadratic function is given. Determine the function's equation. -

Write the equation of a polynomial function with the given characteristics. Use a leading coefficient of 1 or -1 and make the degree of the function as small as possible. -Touches the xxx -axis at 0 and crosses the xxx -axis at 4 ; lies above the xxx -axis between 0 and 4 .

Use the vertex and intercepts to sketch the graph of the quadratic function. - f(x)=−x2+4x+5f ( x ) = - x ^ { 2 } + 4 x + 5f(x)=−x2+4x+5

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - f(x)=3x2−6x−5f ( x ) = 3 x ^ { 2 } - 6 x - 5f(x)=3x2−6x−5

Find the degree of the polynomial function. - g(x)=10x4+2g ( x ) = 10 x ^ { 4 } + 2g(x)=10x4+2

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - y+4=(x+2)2y + 4 = ( x + 2 ) ^ { 2 }y+4=(x+2)2

Find the y-intercept for the graph of the quadratic function. - y+9=(x+3)2y + 9 = ( x + 3 ) ^ { 2 }y+9=(x+3)2

Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. - f(x)=−x3(x+3)2(x−8)f ( x ) = - x ^ { 3 } ( x + 3 ) ^ { 2 } ( x - 8 )f(x)=−x3(x+3)2(x−8)

Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. - f(x)=(x+1)(x−2)(x−1)2f ( x ) = ( x + 1 ) ( x - 2 ) ( x - 1 ) ^ { 2 }f(x)=(x+1)(x−2)(x−1)2

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - f(x)=x2+6f ( x ) = x ^ { 2 } + 6f(x)=x2+6

Find the domain and range of the quadratic function whose graph is described. -The maximum is −6- 6−6 at x=−1x = - 1x=−1

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. - f(x)=x3−4x2+2x+3f ( x ) = x ^ { 3 } - 4 x ^ { 2 } + 2 x + 3f(x)=x3−4x2+2x+3

Find the y-intercept for the graph of the quadratic function. - f(x)=4x2−3x−7f ( x ) = 4 x ^ { 2 } - 3 x - 7f(x)=4x2−3x−7

Determine whether the function is a polynomial function. - f(x)=πx3−2x2−1f ( x ) = \pi x ^ { 3 } - 2 x ^ { 2 } - 1f(x)=πx3−2x2−1

Determine the maximum possible number of turning points for the graph of the function. - y(x)=4x+4y ( x ) = 4 x + 4y(x)=4x+4

Use the vertex and intercepts to sketch the graph of the quadratic function. - f(x)=4−(x−2)2f ( x ) = 4 - ( x - 2 ) ^ { 2 }f(x)=4−(x−2)2

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. - f(x)=(x−1)(x+1)(x+3)3f ( x ) = ( x - 1 ) ( x + 1 ) ( x + 3 ) ^ { 3 }f(x)=(x−1)(x+1)(x+3)3