Question 1

Determine whether the function is a polynomial function.
-$$f ( x ) = \sqrt [ 4 ] { x ^ { 5 } } - x ^ { 6 } - 8$$

Accepted Answer

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

Question 2

Determine whether the function is a polynomial function.
-$$f ( x ) = 4 x + 6 x ^ { 2 }$$

Accepted Answer

A)  $\mathrm { No }$ 
B)  Yes 
A)  $\mathrm { No }$ 
B)  Yes

Question 3

Solve the problem
-A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. 600 feet of fencing is used. Find the dimensions of the playground that maximize the total Enclosed area.

Accepted Answer

A) 150 ft by 150 ft 
B) 50 ft by 225 ft 
C) 100 ft by 150 ft 
D) 75 ft by 150 ft 
A) 150 ft by 150 ft 
B) 50 ft by 225 ft 
C) 100 ft by 150 ft 
D) 75 ft by 150 ft

Question 4

Solve the problem
-The daily profit in dollars of a specialty cake shop is described by the function $P ( x ) = - 4 x ^ { 2 } + 208 x - 1920$, where $x$ is the number of cakes prepared in one day. The maximum profit for the company occurs at the vertex of the parabola. How many cakes should be prepared per day in order to maximize profit?

Accepted Answer

A)  2704 cakes 
B)  26 cakes 
C)  $676 \mathrm { cakes }$ 
D)  $52 \mathrm { cakes }$ 
A)  2704 cakes 
B)  26 cakes 
C)  $676 \mathrm { cakes }$ 
D)  $52 \mathrm { cakes }$

Question 5

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

Accepted Answer

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

Question 6

Find the y-intercept of the polynomial function.
-$$f ( x ) = - x ^ { 2 } ( x + 9 ) \left( x ^ { 2 } + 1 \right)$$

Accepted Answer

A)  $- 9$ 
B)  9 
C)  0 
D)  1 
A)  $- 9$ 
B)  9 
C)  0 
D)  1

Question 7

Find the range of the quadratic function.
-$$f ( x ) = 6 - ( x + 2 ) ^ { 2 }$$

Accepted Answer

A)  $[ - 2 , \infty )$ 
B)  $( - \infty , 6 ]$ 
C)  $( - \infty , 2 ]$ 
D)  $[ 6 , \infty )$ 
A)  $[ - 2 , \infty )$ 
B)  $( - \infty , 6 ]$ 
C)  $( - \infty , 2 ]$ 
D)  $[ 6 , \infty )$

Question 8

Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither.
-$$f ( x ) = ( x - 2 ) ^ { 2 } \left( x ^ { 2 } - 16 \right)$$

Accepted Answer

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

Question 9

Use the vertex and intercepts to sketch the graph of the quadratic function.
-$f ( x ) = x ^ { 2 } + 6 x + 8$

Accepted Answer

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

Question 10

Use the vertex and intercepts to sketch the graph of the quadratic function.
-$f ( x ) = 2 x ^ { 2 } + 20 x + 56$

Accepted Answer

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

Question 11

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.
-$$f ( x ) = x ^ { 2 } ( x - 5 ) ( x - 6 )$$

Accepted Answer

A)  0 , touches the $x$-axis and turns around;
5 , crosses the $x$-axis;
6 , crosses the $x$-axis 
B)  0 , touches the $x$-axis and turns around;
$- 5$, crosses the $x$-axis;
$- 6$, crosses the $x$-axis 
C)  0 , crosses the $x$-axis;
5 , touches the $x$-axis and turns around;
6 , touches the $x$-axis and turns around 
D)  0 , crosses the $x$-axis;
5 , crosses the $x$-axis;
6 , crosses the $x$-axis 
A)  0 , touches the $x$-axis and turns around;
5 , crosses the $x$-axis;
6 , crosses the $x$-axis 
B)  0 , touches the $x$-axis and turns around;
$- 5$, crosses the $x$-axis;
$- 6$, crosses the $x$-axis 
C)  0 , crosses the $x$-axis;
5 , touches the $x$-axis and turns around;
6 , touches the $x$-axis and turns around 
D)  0 , crosses the $x$-axis;
5 , crosses the $x$-axis;
6 , crosses the $x$-axis

Question 12

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

Accepted Answer

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

Question 13

Find the axis of symmetry of the parabola defined by the given quadratic function.
-$$f ( x ) = 8 - ( x + 2 ) ^ { 2 }$$

Accepted Answer

A)  $x = 2$ 
B)  $x = - 2$ 
C)  $x = 8$ 
D)  $x = - 8$ 
A)  $x = 2$ 
B)  $x = - 2$ 
C)  $x = 8$ 
D)  $x = - 8$

Question 14

Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither.
-$$f ( x ) = x ^ { 3 } + 11 x ^ { 2 } + 39 x + 45$$

Accepted Answer

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

Question 15

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the
x-axis or touches the x-axis and turns around, at each zero.
-$$f ( x ) = 2 \left( x - \frac { 5 } { 2 } \right) ( x - 4 ) ^ { 3 }$$

Accepted Answer

A)  $- \frac { 5 } { 2 }$, multiplicity 1 , touches the $x$-axis and turns around; $- 4$, multiplicity 3 , touches $x$-axis and turns around 
B)  $\frac { 5 } { 2 }$, multiplicity 1 , touches the $x$-axis and turns around; 4 , multiplicity 3 , touches $x$-axis and turns around 
C)  $\frac { 5 } { 2 }$, multiplicity 1 , crosses $x$-axis; 4 , multiplicity 3 , crosses $x$-axis 
D)  $- \frac { 5 } { 2 }$, multiplicity 1 , crosses $x$-axis; $- 4$, multiplicity 3 , crosses $x$-axis 
A)  $- \frac { 5 } { 2 }$, multiplicity 1 , touches the $x$-axis and turns around; $- 4$, multiplicity 3 , touches $x$-axis and turns around 
B)  $\frac { 5 } { 2 }$, multiplicity 1 , touches the $x$-axis and turns around; 4 , multiplicity 3 , touches $x$-axis and turns around 
C)  $\frac { 5 } { 2 }$, multiplicity 1 , crosses $x$-axis; 4 , multiplicity 3 , crosses $x$-axis 
D)  $- \frac { 5 } { 2 }$, multiplicity 1 , crosses $x$-axis; $- 4$, multiplicity 3 , crosses $x$-axis

Question 16

Find the range of the quadratic function.
-$$f ( x ) = ( x + 3 ) ^ { 2 } + 7$$

Accepted Answer

A)  $[ 3 , \infty )$ 
B)  $[ 7 , \infty )$ 
C)  $[ - 3 , \infty )$ 
D)  $[ - 7 , \infty )$ 
A)  $[ 3 , \infty )$ 
B)  $[ 7 , \infty )$ 
C)  $[ - 3 , \infty )$ 
D)  $[ - 7 , \infty )$

Question 17

Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given
integers
-$f ( x ) = 8 x ^ { 4 } - 7 x ^ { 2 } - 2$; between 1 and 2

Accepted Answer

A)  $f ( 1 ) = 1$ and $f ( 2 ) = - 98$; yes 
B)  $f ( 1 ) = - 1$ and $f ( 2 ) = 98$; yes 
C)  $f ( 1 ) = 1$ and $f ( 2 ) = 99$; no 
D)  $f ( 1 ) = - 1$ and $f ( 2 ) = - 98$; no 
A)  $f ( 1 ) = 1$ and $f ( 2 ) = - 98$; yes 
B)  $f ( 1 ) = - 1$ and $f ( 2 ) = 98$; yes 
C)  $f ( 1 ) = 1$ and $f ( 2 ) = 99$; no 
D)  $f ( 1 ) = - 1$ and $f ( 2 ) = - 98$; no

Question 18

Graph the polynomial function.
-$f(x)=2 x^{2}-x^{3}$

Accepted Answer

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

Question 19

Find the range of the quadratic function.
-$$f ( x ) = ( x + 7 ) ^ { 2 } - 6$$

Accepted Answer

A)  $[ - 6 , \infty )$ 
B)  $( - \infty , - 6 ]$ 
C)  $[ - 7 , \infty )$ 
D)  $( - \infty , - 7 ]$ 
A)  $[ - 6 , \infty )$ 
B)  $( - \infty , - 6 ]$ 
C)  $[ - 7 , \infty )$ 
D)  $( - \infty , - 7 ]$

Question 20

Find the range of the quadratic function.
-$$f ( x ) = x ^ { 2 } - 4 x - 5$$

Accepted Answer

A)  $( - \infty , - 9 ]$ 
B)  $[ - 2 , \infty )$ 
C)  $[ - 9 , \infty )$ 
D)  $( - \infty , - 17 ]$ 
A)  $( - \infty , - 9 ]$ 
B)  $[ - 2 , \infty )$ 
C)  $[ - 9 , \infty )$ 
D)  $( - \infty , - 17 ]$

Determine whether the function is a polynomial function. - $f ( x ) = \sqrt [ 4 ] { x ^ { 5 } } - x ^ { 6 } - 8$

Determine whether the function is a polynomial function. - $f ( x ) = 4 x + 6 x ^ { 2 }$

Solve the problem -A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. 600 feet of fencing is used. Find the dimensions of the playground that maximize the total Enclosed area.

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

Find the y-intercept of the polynomial function. - $f ( x ) = - x ^ { 2 } ( x + 9 ) \left( x ^ { 2 } + 1 \right)$

Find the range of the quadratic function. - $f ( x ) = 6 - ( x + 2 ) ^ { 2 }$

Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. - $f ( x ) = ( x - 2 ) ^ { 2 } \left( x ^ { 2 } - 16 \right)$

Use the vertex and intercepts to sketch the graph of the quadratic function. - $f ( x ) = x ^ { 2 } + 6 x + 8$ $Use the vertex and intercepts to sketch the graph of the quadratic function. - f ( x ) = x ^ { 2 } + 6 x + 8$

Use the vertex and intercepts to sketch the graph of the quadratic function. - $f ( x ) = 2 x ^ { 2 } + 20 x + 56$ $Use the vertex and intercepts to sketch the graph of the quadratic function. - f ( x ) = 2 x ^ { 2 } + 20 x + 56$

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. - $f ( x ) = x ^ { 2 } ( x - 5 ) ( x - 6 )$

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

Find the axis of symmetry of the parabola defined by the given quadratic function. - $f ( x ) = 8 - ( x + 2 ) ^ { 2 }$

Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. - $f ( x ) = x ^ { 3 } + 11 x ^ { 2 } + 39 x + 45$

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. - $f ( x ) = 2 \left( x - \frac { 5 } { 2 } \right) ( x - 4 ) ^ { 3 }$

Find the range of the quadratic function. - $f ( x ) = ( x + 3 ) ^ { 2 } + 7$

Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given integers - $f ( x ) = 8 x ^ { 4 } - 7 x ^ { 2 } - 2$ ; between 1 and 2

Graph the polynomial function. - $f(x)=2 x^{2}-x^{3}$ $Graph the polynomial function. - f(x)=2 x^{2}-x^{3}$

Find the range of the quadratic function. - $f ( x ) = ( x + 7 ) ^ { 2 } - 6$

Find the range of the quadratic function. - $f ( x ) = x ^ { 2 } - 4 x - 5$

Equations and Inequalities

Functions and Graphs

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Filters

Exam 3: Polynomial and Rational Functions

Determine whether the function is a polynomial function. - f(x)=x54−x6−8f ( x ) = \sqrt [ 4 ] { x ^ { 5 } } - x ^ { 6 } - 8f(x)=4x5​−x6−8

Determine whether the function is a polynomial function. - f(x)=4x+6x2f ( x ) = 4 x + 6 x ^ { 2 }f(x)=4x+6x2

Solve the problem -A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. 600 feet of fencing is used. Find the dimensions of the playground that maximize the total Enclosed area.

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

Find the y-intercept of the polynomial function. - f(x)=−x2(x+9)(x2+1)f ( x ) = - x ^ { 2 } ( x + 9 ) \left( x ^ { 2 } + 1 \right)f(x)=−x2(x+9)(x2+1)

Find the range of the quadratic function. - f(x)=6−(x+2)2f ( x ) = 6 - ( x + 2 ) ^ { 2 }f(x)=6−(x+2)2

Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. - f(x)=(x−2)2(x2−16)f ( x ) = ( x - 2 ) ^ { 2 } \left( x ^ { 2 } - 16 \right)f(x)=(x−2)2(x2−16)

Use the vertex and intercepts to sketch the graph of the quadratic function. - f(x)=x2+6x+8f ( x ) = x ^ { 2 } + 6 x + 8f(x)=x2+6x+8

Use the vertex and intercepts to sketch the graph of the quadratic function. - f(x)=2x2+20x+56f ( x ) = 2 x ^ { 2 } + 20 x + 56f(x)=2x2+20x+56

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−5)(x−6)f ( x ) = x ^ { 2 } ( x - 5 ) ( x - 6 )f(x)=x2(x−5)(x−6)

Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. - f(x)=x(2−x2)f ( x ) = x \left( 2 - x ^ { 2 } \right)f(x)=x(2−x2)

Find the axis of symmetry of the parabola defined by the given quadratic function. - f(x)=8−(x+2)2f ( x ) = 8 - ( x + 2 ) ^ { 2 }f(x)=8−(x+2)2

Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. - f(x)=x3+11x2+39x+45f ( x ) = x ^ { 3 } + 11 x ^ { 2 } + 39 x + 45f(x)=x3+11x2+39x+45

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. - f(x)=2(x−52)(x−4)3f ( x ) = 2 \left( x - \frac { 5 } { 2 } \right) ( x - 4 ) ^ { 3 }f(x)=2(x−25​)(x−4)3

Find the range of the quadratic function. - f(x)=(x+3)2+7f ( x ) = ( x + 3 ) ^ { 2 } + 7f(x)=(x+3)2+7

Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given integers - f(x)=8x4−7x2−2f ( x ) = 8 x ^ { 4 } - 7 x ^ { 2 } - 2f(x)=8x4−7x2−2 ; between 1 and 2

Graph the polynomial function. - f(x)=2x2−x3f(x)=2 x^{2}-x^{3}f(x)=2x2−x3

Find the range of the quadratic function. - f(x)=(x+7)2−6f ( x ) = ( x + 7 ) ^ { 2 } - 6f(x)=(x+7)2−6

Find the range of the quadratic function. - f(x)=x2−4x−5f ( x ) = x ^ { 2 } - 4 x - 5f(x)=x2−4x−5

Equations and Inequalities

Functions and Graphs

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Filters

Determine whether the function is a polynomial function. - $f ( x ) = \sqrt [ 4 ] { x ^ { 5 } } - x ^ { 6 } - 8$

Determine whether the function is a polynomial function. - $f ( x ) = 4 x + 6 x ^ { 2 }$

Find the y-intercept of the polynomial function. - $f ( x ) = - x ^ { 2 } ( x + 9 ) \left( x ^ { 2 } + 1 \right)$

Find the range of the quadratic function. - $f ( x ) = 6 - ( x + 2 ) ^ { 2 }$

Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. - $f ( x ) = ( x - 2 ) ^ { 2 } \left( x ^ { 2 } - 16 \right)$

Use the vertex and intercepts to sketch the graph of the quadratic function. - $f ( x ) = x ^ { 2 } + 6 x + 8$ $Use the vertex and intercepts to sketch the graph of the quadratic function. - f ( x ) = x ^ { 2 } + 6 x + 8$

Use the vertex and intercepts to sketch the graph of the quadratic function. - $f ( x ) = 2 x ^ { 2 } + 20 x + 56$ $Use the vertex and intercepts to sketch the graph of the quadratic function. - f ( x ) = 2 x ^ { 2 } + 20 x + 56$

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. - $f ( x ) = x ^ { 2 } ( x - 5 ) ( x - 6 )$

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

Find the axis of symmetry of the parabola defined by the given quadratic function. - $f ( x ) = 8 - ( x + 2 ) ^ { 2 }$

Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. - $f ( x ) = x ^ { 3 } + 11 x ^ { 2 } + 39 x + 45$

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. - $f ( x ) = 2 \left( x - \frac { 5 } { 2 } \right) ( x - 4 ) ^ { 3 }$

Find the range of the quadratic function. - $f ( x ) = ( x + 3 ) ^ { 2 } + 7$

Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given integers - $f ( x ) = 8 x ^ { 4 } - 7 x ^ { 2 } - 2$ ; between 1 and 2

Graph the polynomial function. - $f(x)=2 x^{2}-x^{3}$ $Graph the polynomial function. - f(x)=2 x^{2}-x^{3}$

Find the range of the quadratic function. - $f ( x ) = ( x + 7 ) ^ { 2 } - 6$

Find the range of the quadratic function. - $f ( x ) = x ^ { 2 } - 4 x - 5$