Question 1

Solve.
-Suppose that a polynomial function is used to model the data shown in the graph below.  
For what intervals is the function increasing?

Accepted Answer

A)  10 through 25 and 40 through 50 
B)  0 through 40 
C)  0 through 10 and 20 through 50 
D)  0 through 10 and 25 through 40 
A)  10 through 25 and 40 through 50 
B)  0 through 40 
C)  0 through 10 and 20 through 50 
D)  0 through 10 and 25 through 40

Question 2

Find the coordinates of the vertex for the parabola defined by the given quadratic function.
-$$f ( x ) = 6 - ( x + 4 ) ^ { 2 }$$

Accepted Answer

A)  $( 4,6 )$ 
B)  $( 6 , - 4 )$ 
C)  $( - 4,6 )$ 
D)  $( 6,4 )$ 
A)  $( 4,6 )$ 
B)  $( 6 , - 4 )$ 
C)  $( - 4,6 )$ 
D)  $( 6,4 )$

Question 3

Solve the problem
-Among all pairs of numbers whose difference is 36, find a pair whose product is as small as possible.

Accepted Answer

A) 18 and 18 
B) -18 and 18 
C) -54 and -18 
D) 54 and 18 
A) 18 and 18 
B) -18 and 18 
C) -54 and -18 
D) 54 and 18

Question 4

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.
-$$f ( x ) = \left( x + \frac { 1 } { 5 } \right) ^ { 4 } \left( x ^ { 2 } + 7 \right) ^ { 5 }$$

Accepted Answer

A)  $- \frac { 1 } { 5 }$, multiplicity 4 , crosses the $x$-axis. 
B)  $- \frac { 1 } { 5 }$, multiplicity 4 , touches the $x$-axis and turns around; $- 7$, multiplicity 5 , crosses the $x$-axis 
C)  $\frac { 1 } { 5 }$, multiplicity 4 , touches the $x$-axis and turns around; 7 , multiplicity 5 , crosses the $x$-axis 
D)  $- \frac { 1 } { 5 }$, multiplicity 4 , touches the $x$-axis and turns around. 
A)  $- \frac { 1 } { 5 }$, multiplicity 4 , crosses the $x$-axis. 
B)  $- \frac { 1 } { 5 }$, multiplicity 4 , touches the $x$-axis and turns around; $- 7$, multiplicity 5 , crosses the $x$-axis 
C)  $\frac { 1 } { 5 }$, multiplicity 4 , touches the $x$-axis and turns around; 7 , multiplicity 5 , crosses the $x$-axis 
D)  $- \frac { 1 } { 5 }$, multiplicity 4 , touches the $x$-axis and turns around.

Question 5

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

Accepted Answer

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

Question 6

Find the zeros of the polynomial function
-$$f ( x ) = x ^ { 3 } + x ^ { 2 } - 20 x$$

Accepted Answer

A)  $x = 3 , x = 4$ 
B)  $x = 0 , x = 3 , x = 4$ 
C)  $x = - 5 , x = 4$ 
D)  $x = 0 , x = - 5 , x = 4$ 
A)  $x = 3 , x = 4$ 
B)  $x = 0 , x = 3 , x = 4$ 
C)  $x = - 5 , x = 4$ 
D)  $x = 0 , x = - 5 , x = 4$

Question 7

Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither.
-$$x ^ { 5 } - 7 x ^ { 3 } + 6 x = 0$$

Accepted Answer

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

Question 8

Solve the problem
-An arrow is fired into the air with an initial velocity of 96 feet per second. The height in feet of the arrow t seconds after it was shot into the air is given by the function $h ( x ) = - 16 t ^ { 2 } + 96 t$. Find the maximum height of the arrow.

Accepted Answer

A)  $432 \mathrm { ft }$ 
B)  $144 \mathrm { ft }$ 
C)  $48 \mathrm { ft }$ 
D)  $240 \mathrm { ft }$ 
A)  $432 \mathrm { ft }$ 
B)  $144 \mathrm { ft }$ 
C)  $48 \mathrm { ft }$ 
D)  $240 \mathrm { ft }$

Question 9

Solve the problem.
-Write an equation in standard form of the parabola that has the same shape as the graph of  f(x)=11 x2 , but which has its vertex at  (2,5) .

Accepted Answer

A)  $f ( x ) = 11 ( x + 2 ) ^ { 2 } + 5$ 
B)  $f ( x ) = ( 11 x + 2 ) ^ { 2 } + 5$ 
C)  $f ( x ) = 11 ( x - 2 ) ^ { 2 } + 5$ 
D)  $f ( x ) = 11 ( x + 5 ) ^ { 2 } + 2$ 
A)  $f ( x ) = 11 ( x + 2 ) ^ { 2 } + 5$ 
B)  $f ( x ) = ( 11 x + 2 ) ^ { 2 } + 5$ 
C)  $f ( x ) = 11 ( x - 2 ) ^ { 2 } + 5$ 
D)  $f ( x ) = 11 ( x + 5 ) ^ { 2 } + 2$

Question 10

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

Accepted Answer

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

Question 11

Find the degree of the polynomial function.
-$$f ( x ) = \frac { 1 - x ^ { 5 } } { 5 }$$

Accepted Answer

A)  1 
B)  $- \frac { 1 } { 5 }$ 
C)  5 
D)  0 
A)  1 
B)  $- \frac { 1 } { 5 }$ 
C)  5 
D)  0

Question 12

Find the y-intercept of the polynomial function.
-$$f ( x ) = ( x - 3 ) ^ { 2 } \left( x ^ { 2 } - 16 \right)$$

Accepted Answer

A)  $- 48$ 
B)  48 
C)  144 
D)  $- 144$ 
A)  $- 48$ 
B)  48 
C)  144 
D)  $- 144$

Question 13

Use the Leading Coefficient Test to determine the end behavior of the polynomial function.
-$$( x ) = - 6 x ^ { 3 } ( x + 1 ) ( x + 4 ) ^ { 2 }$$

Accepted Answer

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

Question 14

Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither.
-

Accepted Answer

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

Question 15

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.
-$$f ( x ) = x ^ { 4 } - 36 x ^ { 2 }$$

Accepted Answer

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

Question 16

Graph the polynomial function.
-$$f ( x ) = x ^ { 4 } - 4 x ^ { 2 }$$

Accepted Answer

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

Question 17

Find the axis of symmetry of the parabola defined by the given quadratic function.
-$$f ( x ) = x ^ { 2 } + 14 x - 8$$

Accepted Answer

A)  $x = - 7$ 
B)  $x = 7$ 
C)  $x = - 57$ 
D)  $x = 14$ 
A)  $x = - 7$ 
B)  $x = 7$ 
C)  $x = - 57$ 
D)  $x = 14$

Question 18

Solve the problem
-Among all pairs of numbers whose sum is 68, find a pair whose product is as large as possible.

Accepted Answer

A) 36 and 32 
B) 34 and 34 
C) 17 and 17 
D) 67 and 1 
A) 36 and 32 
B) 34 and 34 
C) 17 and 17 
D) 67 and 1

Question 19

Find the domain and range of the quadratic function whose graph is described.
-The vertex is $( 1,0 )$ and the graph opens down.

Accepted Answer

A)  Domain: $( - \infty , 1 ]$
Range: $( - \infty , 0 ]$ 
B)  Domain: $( - \infty , \infty )$
Range: $[ 0 , \infty )$ 
C)  Domain: $( - \infty , \infty )$
Range: $( - \infty , 1 ]$ 
D)  Domain: $( - \infty , \infty )$
Range: $( - \infty , 0 ]$ 
A)  Domain: $( - \infty , 1 ]$
Range: $( - \infty , 0 ]$ 
B)  Domain: $( - \infty , \infty )$
Range: $[ 0 , \infty )$ 
C)  Domain: $( - \infty , \infty )$
Range: $( - \infty , 1 ]$ 
D)  Domain: $( - \infty , \infty )$
Range: $( - \infty , 0 ]$

Question 20

Use the vertex and intercepts to sketch the graph of the quadratic function.
-$y - 4 = ( x - 1 ) ^ { 2 }$

Accepted Answer

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

Solve. -Suppose that a polynomial function is used to model the data shown in the graph below. For what intervals is the function increasing?

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = 6 - ( x + 4 ) ^ { 2 }$

Solve the problem -Among all pairs of numbers whose difference is 36, find a pair whose product is as small as possible.

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. - $f ( x ) = \left( x + \frac { 1 } { 5 } \right) ^ { 4 } \left( x ^ { 2 } + 7 \right) ^ { 5 }$

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

Find the zeros of the polynomial function - $f ( x ) = x ^ { 3 } + x ^ { 2 } - 20 x$

Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. - $x ^ { 5 } - 7 x ^ { 3 } + 6 x = 0$

Solve the problem -An arrow is fired into the air with an initial velocity of 96 feet per second. The height in feet of the arrow t seconds after it was shot into the air is given by the function $h ( x ) = - 16 t ^ { 2 } + 96 t$ . Find the maximum height of the arrow.

Solve the problem. -Write an equation in standard form of the parabola that has the same shape as the graph of f(x)=11 x² , but which has its vertex at (2,5) .

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

Find the degree of the polynomial function. - $f ( x ) = \frac { 1 - x ^ { 5 } } { 5 }$

Find the y-intercept of the polynomial function. - $f ( x ) = ( x - 3 ) ^ { 2 } \left( x ^ { 2 } - 16 \right)$

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. - $( x ) = - 6 x ^ { 3 } ( x + 1 ) ( x + 4 ) ^ { 2 }$

Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. -

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. - $f ( x ) = x ^ { 4 } - 36 x ^ { 2 }$

Graph the polynomial function. - $f ( x ) = x ^ { 4 } - 4 x ^ { 2 }$ $Graph the polynomial function. - f ( x ) = x ^ { 4 } - 4 x ^ { 2 }$

Find the axis of symmetry of the parabola defined by the given quadratic function. - $f ( x ) = x ^ { 2 } + 14 x - 8$

Solve the problem -Among all pairs of numbers whose sum is 68, find a pair whose product is as large as possible.

Find the domain and range of the quadratic function whose graph is described. -The vertex is $( 1,0 )$ and the graph opens down.

Use the vertex and intercepts to sketch the graph of the quadratic function. - $y - 4 = ( x - 1 ) ^ { 2 }$ $Use the vertex and intercepts to sketch the graph of the quadratic function. - y - 4 = ( x - 1 ) ^ { 2 }$

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Exam 3: Polynomial and Rational Functions

Solve. -Suppose that a polynomial function is used to model the data shown in the graph below. For what intervals is the function increasing?

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - f(x)=6−(x+4)2f ( x ) = 6 - ( x + 4 ) ^ { 2 }f(x)=6−(x+4)2

Solve the problem -Among all pairs of numbers whose difference is 36, find a pair whose product is as small as possible.

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

Find the zeros of the polynomial function - f(x)=x3+x2−20xf ( x ) = x ^ { 3 } + x ^ { 2 } - 20 xf(x)=x3+x2−20x

Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. - x5−7x3+6x=0x ^ { 5 } - 7 x ^ { 3 } + 6 x = 0x5−7x3+6x=0

Solve the problem -An arrow is fired into the air with an initial velocity of 96 feet per second. The height in feet of the arrow t seconds after it was shot into the air is given by the function h(x)=−16t2+96th ( x ) = - 16 t ^ { 2 } + 96 th(x)=−16t2+96t . Find the maximum height of the arrow.

Solve the problem. -Write an equation in standard form of the parabola that has the same shape as the graph of f(x)=11 x2 , but which has its vertex at (2,5) .

Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. - f(x)=3−x4f ( x ) = 3 - x ^ { 4 }f(x)=3−x4

Find the degree of the polynomial function. - f(x)=1−x55f ( x ) = \frac { 1 - x ^ { 5 } } { 5 }f(x)=51−x5​

Find the y-intercept of the polynomial function. - f(x)=(x−3)2(x2−16)f ( x ) = ( x - 3 ) ^ { 2 } \left( x ^ { 2 } - 16 \right)f(x)=(x−3)2(x2−16)

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. - (x)=−6x3(x+1)(x+4)2( x ) = - 6 x ^ { 3 } ( x + 1 ) ( x + 4 ) ^ { 2 }(x)=−6x3(x+1)(x+4)2