Question 1

Find the range of the quadratic function.
-$$f ( x ) = 2 x ^ { 2 } + 2 x - 8$$

Accepted Answer

A)  $\left( - \infty , - \frac { 1 } { 2 } \right]$ 
B)  $\left( - \infty , - \frac { 17 } { 2 } \right]$ 
C)  $\left[ - \frac { 17 } { 2 } , \infty \right)$ 
D)  $\left[ - \frac { 1 } { 2 } , \infty \right)$ 
A)  $\left( - \infty , - \frac { 1 } { 2 } \right]$ 
B)  $\left( - \infty , - \frac { 17 } { 2 } \right]$ 
C)  $\left[ - \frac { 17 } { 2 } , \infty \right)$ 
D)  $\left[ - \frac { 1 } { 2 } , \infty \right)$

Question 2

Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of
the minimum or maximum point.
-$$f ( x ) = - 2 x ^ { 2 } + 6 x$$

Accepted Answer

A)  minimum; $\left( - \frac { 3 } { 2 } , - \frac { 9 } { 2 } \right)$ 
B)  minimum; $\left( \frac { 3 } { 2 } , \frac { 9 } { 2 } \right)$ 
C)  maximum; $\left( - \frac { 3 } { 2 } , - \frac { 9 } { 2 } \right)$ 
D)  maximum; $\left( \frac { 3 } { 2 } , \frac { 9 } { 2 } \right)$ 
A)  minimum; $\left( - \frac { 3 } { 2 } , - \frac { 9 } { 2 } \right)$ 
B)  minimum; $\left( \frac { 3 } { 2 } , \frac { 9 } { 2 } \right)$ 
C)  maximum; $\left( - \frac { 3 } { 2 } , - \frac { 9 } { 2 } \right)$ 
D)  maximum; $\left( \frac { 3 } { 2 } , \frac { 9 } { 2 } \right)$

Question 3

Use the vertex and intercepts to sketch the graph of the quadratic function.
-$f ( x ) = - 2 x - 3 + x ^ { 2 }$

Accepted Answer

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

Question 4

Determine whether the graph shown is the graph of a polynomial function.
-

Accepted Answer

A) not a polynomial function 
B) polynomial function 
A) not a polynomial function 
B) polynomial function

Question 5

Find the x-intercepts (if any) for the graph of the quadratic function.
-$$f ( x ) = - x ^ { 2 } + 7 x - 12$$

Accepted Answer

A)  $( 3,0 )$ and $( - 4,0 )$ 
B)  No x-intercepts 
C)  $( 3,0 )$ and $( 4,0 )$ 
D)  $( - 3,0 )$ and $( - 4,0 )$ 
A)  $( 3,0 )$ and $( - 4,0 )$ 
B)  No x-intercepts 
C)  $( 3,0 )$ and $( 4,0 )$ 
D)  $( - 3,0 )$ and $( - 4,0 )$

Question 6

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end behavior
to match the function with its graph.
-$$f ( x ) = 4 x ^ { 3 } - 3 x ^ { 2 } - 2 x - 3$$

Accepted Answer

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

Question 7

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.
-$$f ( x ) = 6 x ^ { 2 } - x ^ { 3 }$$

Accepted Answer

A)  0 , touches the $x$-axis and turns around;
6 , crosses the $x$-axis 
B)  0 , crosses the $x$-axis;
$\sqrt { 6 }$, crosses the $x$-axis;
$- \sqrt { 6 }$, crosses the $x$-axis 
C)  0 , touches the $x$-axis and turns around;
6 , touches the $x$-axis and turns around 
D)  0 , touches the $x$-axis and turns around;
$\sqrt { 6 }$, crosses the $x$-axis;
$- \sqrt { 6 }$, crosses the $x$-axis 
A)  0 , touches the $x$-axis and turns around;
6 , crosses the $x$-axis 
B)  0 , crosses the $x$-axis;
$\sqrt { 6 }$, crosses the $x$-axis;
$- \sqrt { 6 }$, crosses the $x$-axis 
C)  0 , touches the $x$-axis and turns around;
6 , touches the $x$-axis and turns around 
D)  0 , touches the $x$-axis and turns around;
$\sqrt { 6 }$, crosses the $x$-axis;
$- \sqrt { 6 }$, crosses the $x$-axis

Question 8

Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither.
-$$f ( x ) = - x ^ { 3 } ( x + 1 ) ^ { 2 } ( x - 6 )$$

Accepted Answer

A)  $\mathrm { y }$-axis symmetry 
B)  origin symmetry 
C)  neither 
A)  $\mathrm { y }$-axis symmetry 
B)  origin symmetry 
C)  neither

Question 9

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.
-$$f ( x ) = - x ^ { 2 } ( x + 4 ) \left( x ^ { 2 } + 1 \right)$$

Accepted Answer

A)  0 , touches the $x$-axis and turns around;
4 , crosses the $x$-axis 
B)  0 , touches the $x$-axis and turns around; 
$- 4$, crosses the $x$-axis;
$- 1$, crosses the x-axis;
1, crosses the x-axis; 
C)  0 , touches the $x$-axis and turns around;
$- 4$, crosses the $x$-axis 
D)  0 , touches the $x$-axis and turns around; 
 $- 4$, crosses the $x$-axis;
$- 1$, touches the $x$-axis and turns around 
A)  0 , touches the $x$-axis and turns around;
4 , crosses the $x$-axis 
B)  0 , touches the $x$-axis and turns around; 
$- 4$, crosses the $x$-axis;
$- 1$, crosses the x-axis;
1, crosses the x-axis; 
C)  0 , touches the $x$-axis and turns around;
$- 4$, crosses the $x$-axis 
D)  0 , touches the $x$-axis and turns around; 
 $- 4$, crosses the $x$-axis;
$- 1$, touches the $x$-axis and turns around

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.
-$$x ^ { 4 } + 3 x ^ { 3 } - 10 x ^ { 2 } = 0$$

Accepted Answer

A)  0 , touches the $x$-axis and turns around;
5 , crosses the $x$-axis;
$- 2$, crosses the $x$-axis 
B)  0 , touches the $x$-axis and turns around;
5 , touches the $x$-axis and turns around;
$- 2$, touches the $x$-axis and turns around 
C)  0 , crosses the $x$-axis;
$- 5$, crosses the $x$-axis;
2 , crosses the $x$-axis 
D)  0 , touches the $x$-axis and turns around;
$- 5$, crosses the $x$-axis;
2 , crosses the $x$-axis 
A)  0 , touches the $x$-axis and turns around;
5 , crosses the $x$-axis;
$- 2$, crosses the $x$-axis 
B)  0 , touches the $x$-axis and turns around;
5 , touches the $x$-axis and turns around;
$- 2$, touches the $x$-axis and turns around 
C)  0 , crosses the $x$-axis;
$- 5$, crosses the $x$-axis;
2 , crosses the $x$-axis 
D)  0 , touches the $x$-axis and turns around;
$- 5$, crosses the $x$-axis;
2 , crosses the $x$-axis

Question 11

Determine the maximum possible number of turning points for the graph of the function.
-$$f ( x ) = x ^ { 7 } + 3 x ^ { 8 }$$

Accepted Answer

A)  1 
B)  7 
C)  3 
D)  8 
A)  1 
B)  7 
C)  3 
D)  8

Question 12

Find the axis of symmetry of the parabola defined by the given quadratic function.
-$$f ( x ) = 11 ( x - 3 ) ^ { 2 } + 5$$

Accepted Answer

A)  $x = - 3$ 
B)  $x = 3$ 
C)  $x = 11$ 
D)  $x = 5$ 
A)  $x = - 3$ 
B)  $x = 3$ 
C)  $x = 11$ 
D)  $x = 5$

Question 13

Find the range of the quadratic function.
-$$f ( x ) = - 5 x ^ { 2 } + 15 x$$

Accepted Answer

A)  $\left( - \infty , \frac { 3 } { 2 } \right]$ 
B)  $\left( - \infty , \frac { 45 } { 4 } \right]$ 
C)  $\left( - \infty , - \frac { 3 } { 2 } \right]$ 
D)  $\left( - \infty , - \frac { 45 } { 4 } \right]$ 
A)  $\left( - \infty , \frac { 3 } { 2 } \right]$ 
B)  $\left( - \infty , \frac { 45 } { 4 } \right]$ 
C)  $\left( - \infty , - \frac { 3 } { 2 } \right]$ 
D)  $\left( - \infty , - \frac { 45 } { 4 } \right]$

Question 14

Find the axis of symmetry of the parabola defined by the given quadratic function.
-$$f ( x ) = - 7 ( x - 3 ) ^ { 2 } - 6$$

Accepted Answer

A)  $x = - 3$ 
B)  $x = 3$ 
C)  $x = - 6$ 
D)  $x = - 7$ 
A)  $x = - 3$ 
B)  $x = 3$ 
C)  $x = - 6$ 
D)  $x = - 7$

Question 15

Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither.
-$$f ( x ) = x ^ { 3 } + x ^ { 2 } + 1$$

Accepted Answer

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

Question 16

Solve the problem
-A herd of moose is introduced to a wildlife refuge. The number of moose, $\mathrm { N } ( \mathrm { t } )$, after $\mathrm { t }$ years is described by the polynomial function $N ( t ) = - t ^ { 3 } + 24 t + 80$. Use the Leading Coefficient Test to determine the graph's end behavior. What does this mean about what will eventually happen to the moose population?

Accepted Answer

A)  The moose population in the refuge will grow out of control. 
B)  The moose population in the refuge will reach a constant amount greater than 0 . 
C)  The moose population in the refuge will be displaced by "oil" wells. 
D)  The moose population in the refuge will die out. 
A)  The moose population in the refuge will grow out of control. 
B)  The moose population in the refuge will reach a constant amount greater than 0 . 
C)  The moose population in the refuge will be displaced by "oil" wells. 
D)  The moose population in the refuge will die out.

Question 17

Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither.
-$$f ( x ) = 4 x ^ { 2 } - x ^ { 3 }$$

Accepted Answer

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

Question 18

Solve the problem
-The following table shows the number of speeding tickets issued in a county for the years 1994-1998, where 1 represents 1995, and so on.

This data can be approximated using the third-degree polynomial
$$T ( x ) = - 0.67 x ^ { 3 } + 0.57 x ^ { 2 } + 63.80 x + 4213$$
Use the Leading Coefficient Test to determine the end behavior to the right for the graph of T. Will this function be useful in modeling the number of speeding tickets issued over an extended period of time? Explain your answer.

Accepted Answer

A)  The graph of T decreases without bound to the right. Since the number of larceny thefts will eventually decrease, the function T will be useful in modeling the number of speeding tickets issued over an extended period of time. 
B)  The graph of T decreases without bound to the right. This means that as $x$ increases, the values of $T$ will become more and more negative and the function will no longer model the number of speeding tickets issued. 
C)  The graph of $T$ increases without bound to the right. This means that as $x$ increases, the values of $T$ will become large and positive and, since the values of T will become so large, the function will no longer model the number of speeding tickets issued. 
D)  The graph of $T$ approaches zero for large values of $x$. This means that $T$ will not be useful in modeling the number of speeding tickets issued over an extended period. 
A)  The graph of T decreases without bound to the right. Since the number of larceny thefts will eventually decrease, the function T will be useful in modeling the number of speeding tickets issued over an extended period of time. 
B)  The graph of T decreases without bound to the right. This means that as $x$ increases, the values of $T$ will become more and more negative and the function will no longer model the number of speeding tickets issued. 
C)  The graph of $T$ increases without bound to the right. This means that as $x$ increases, the values of $T$ will become large and positive and, since the values of T will become so large, the function will no longer model the number of speeding tickets issued. 
D)  The graph of $T$ approaches zero for large values of $x$. This means that $T$ will not be useful in modeling the number of speeding tickets issued over an extended period.

Question 19

Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of
the minimum or maximum point.
-$$f ( x ) = 2 x ^ { 2 } - 2 x - 3$$

Accepted Answer

A)  maximum; $\left( \frac { 1 } { 2 } , - \frac { 7 } { 2 } \right)$ 
B)  minimum; $\left( \frac { 1 } { 2 } , - \frac { 7 } { 2 } \right)$ 
C)  maximum; $\left( - \frac { 7 } { 2 } , \frac { 1 } { 2 } \right)$ 
D)  minimum; $\left( - \frac { 7 } { 2 } , \frac { 1 } { 2 } \right)$ 
A)  maximum; $\left( \frac { 1 } { 2 } , - \frac { 7 } { 2 } \right)$ 
B)  minimum; $\left( \frac { 1 } { 2 } , - \frac { 7 } { 2 } \right)$ 
C)  maximum; $\left( - \frac { 7 } { 2 } , \frac { 1 } { 2 } \right)$ 
D)  minimum; $\left( - \frac { 7 } { 2 } , \frac { 1 } { 2 } \right)$

Question 20

Find the coordinates of the vertex for the parabola defined by the given quadratic function.
-$$f ( x ) = ( x + 4 ) ^ { 2 } - 8$$

Accepted Answer

A)  $( - 4 , - 8 )$ 
B)  $( 4 , - 8 )$ 
C)  $( 4,8 )$ 
D)  $( - 4,8 )$ 
A)  $( - 4 , - 8 )$ 
B)  $( 4 , - 8 )$ 
C)  $( 4,8 )$ 
D)  $( - 4,8 )$

Find the range of the quadratic function. - $f ( x ) = 2 x ^ { 2 } + 2 x - 8$

Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of the minimum or maximum point. - $f ( x ) = - 2 x ^ { 2 } + 6 x$

Use the vertex and intercepts to sketch the graph of the quadratic function. - $f ( x ) = - 2 x - 3 + x ^ { 2 }$ $Use the vertex and intercepts to sketch the graph of the quadratic function. - f ( x ) = - 2 x - 3 + x ^ { 2 }$

Determine whether the graph shown is the graph of a polynomial function. -

Find the x-intercepts (if any) for the graph of the quadratic function. - $f ( x ) = - x ^ { 2 } + 7 x - 12$

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end behavior to match the function with its graph. - $f ( x ) = 4 x ^ { 3 } - 3 x ^ { 2 } - 2 x - 3$

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. - $f ( x ) = 6 x ^ { 2 } - x ^ { 3 }$

Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. - $f ( x ) = - x ^ { 3 } ( x + 1 ) ^ { 2 } ( x - 6 )$

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. - $f ( x ) = - x ^ { 2 } ( x + 4 ) \left( x ^ { 2 } + 1 \right)$

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. - $x ^ { 4 } + 3 x ^ { 3 } - 10 x ^ { 2 } = 0$

Determine the maximum possible number of turning points for the graph of the function. - $f ( x ) = x ^ { 7 } + 3 x ^ { 8 }$

Find the axis of symmetry of the parabola defined by the given quadratic function. - $f ( x ) = 11 ( x - 3 ) ^ { 2 } + 5$

Find the range of the quadratic function. - $f ( x ) = - 5 x ^ { 2 } + 15 x$

Find the axis of symmetry of the parabola defined by the given quadratic function. - $f ( x ) = - 7 ( x - 3 ) ^ { 2 } - 6$

Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. - $f ( x ) = x ^ { 3 } + x ^ { 2 } + 1$

Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. - $f ( x ) = 4 x ^ { 2 } - x ^ { 3 }$

Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of the minimum or maximum point. - $f ( x ) = 2 x ^ { 2 } - 2 x - 3$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = ( x + 4 ) ^ { 2 } - 8$

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Exam 3: Polynomial and Rational Functions

Find the range of the quadratic function. - f(x)=2x2+2x−8f ( x ) = 2 x ^ { 2 } + 2 x - 8f(x)=2x2+2x−8

Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of the minimum or maximum point. - f(x)=−2x2+6xf ( x ) = - 2 x ^ { 2 } + 6 xf(x)=−2x2+6x

Use the vertex and intercepts to sketch the graph of the quadratic function. - f(x)=−2x−3+x2f ( x ) = - 2 x - 3 + x ^ { 2 }f(x)=−2x−3+x2

Determine whether the graph shown is the graph of a polynomial function. -

Find the x-intercepts (if any) for the graph of the quadratic function. - f(x)=−x2+7x−12f ( x ) = - x ^ { 2 } + 7 x - 12f(x)=−x2+7x−12

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end behavior to match the function with its graph. - f(x)=4x3−3x2−2x−3f ( x ) = 4 x ^ { 3 } - 3 x ^ { 2 } - 2 x - 3f(x)=4x3−3x2−2x−3

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)=6x2−x3f ( x ) = 6 x ^ { 2 } - x ^ { 3 }f(x)=6x2−x3

Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. - f(x)=−x3(x+1)2(x−6)f ( x ) = - x ^ { 3 } ( x + 1 ) ^ { 2 } ( x - 6 )f(x)=−x3(x+1)2(x−6)

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)=−x2(x+4)(x2+1)f ( x ) = - x ^ { 2 } ( x + 4 ) \left( x ^ { 2 } + 1 \right)f(x)=−x2(x+4)(x2+1)

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. - x4+3x3−10x2=0x ^ { 4 } + 3 x ^ { 3 } - 10 x ^ { 2 } = 0x4+3x3−10x2=0

Determine the maximum possible number of turning points for the graph of the function. - f(x)=x7+3x8f ( x ) = x ^ { 7 } + 3 x ^ { 8 }f(x)=x7+3x8

Find the axis of symmetry of the parabola defined by the given quadratic function. - f(x)=11(x−3)2+5f ( x ) = 11 ( x - 3 ) ^ { 2 } + 5f(x)=11(x−3)2+5

Find the range of the quadratic function. - f(x)=−5x2+15xf ( x ) = - 5 x ^ { 2 } + 15 xf(x)=−5x2+15x

Find the axis of symmetry of the parabola defined by the given quadratic function. - f(x)=−7(x−3)2−6f ( x ) = - 7 ( x - 3 ) ^ { 2 } - 6f(x)=−7(x−3)2−6

Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. - f(x)=x3+x2+1f ( x ) = x ^ { 3 } + x ^ { 2 } + 1f(x)=x3+x2+1

Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. - f(x)=4x2−x3f ( x ) = 4 x ^ { 2 } - x ^ { 3 }f(x)=4x2−x3

Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of the minimum or maximum point. - f(x)=2x2−2x−3f ( x ) = 2 x ^ { 2 } - 2 x - 3f(x)=2x2−2x−3

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - f(x)=(x+4)2−8f ( x ) = ( x + 4 ) ^ { 2 } - 8f(x)=(x+4)2−8