Question 1

Using the graph below, find the domain and range of the given function, and sketch the graph.  
-$y=f(-x)$

Accepted Answer

A)  D: $[ - 4,5 ] ;$ R: $[ - 3,3 ]$
  
B)  D: $[ - 4,5 ] ;$ R: $[ - 3,3 ]$
  
C)  D: $[ - 5,4 ] ;$ R: $[ - 3,3 ]$
  
D)  D: $[ - 4,5 ] ; R : [ - 3,4 ]$
  
A)  D: $[ - 4,5 ] ;$ R: $[ - 3,3 ]$
  
B)  D: $[ - 4,5 ] ;$ R: $[ - 3,3 ]$
  
C)  D: $[ - 5,4 ] ;$ R: $[ - 3,3 ]$
  
D)  D: $[ - 4,5 ] ; R : [ - 3,4 ]$

Question 2

Solve the problem.
-$$\text { Use the angle sum formulas to derive } \sin ( A - B ) = \sin A \cos B - \cos A \sin B \text {. }$$

Accepted Answer

\[\begin{array} { l } 
\sin (

Question 3

Solve the problem.
-Suppose the consumption of electricity grows at 5.8% per year, compounded continuously. Find the number of years before the use of electricity has tripled. Round the answer to the nearest hundredth.

Accepted Answer

A)  18.94 yr 
B)  1.89 yr 
C)  51.72 yr 
D)  0.19 yr 
A)  18.94 yr 
B)  1.89 yr 
C)  51.72 yr 
D)  0.19 yr

Question 4

Find the domain and range of the function.
-$g ( z ) = \frac { - 5 } { \sqrt { z + 1 } }$

Accepted Answer

A)  D: $[ 1 , \infty )$, R: $( - \infty , \infty )$ 
B)  D: $( - 1 , \infty )$, R: $( - \infty , 0 )$ 
C)  D: $( - \infty , - 1 ) , R : ( 0 , \infty )$ 
D)  D: $[ 0 , \infty ) , R : ( - \infty , \infty )$ 
A)  D: $[ 1 , \infty )$, R: $( - \infty , \infty )$ 
B)  D: $( - 1 , \infty )$, R: $( - \infty , 0 )$ 
C)  D: $( - \infty , - 1 ) , R : ( 0 , \infty )$ 
D)  D: $[ 0 , \infty ) , R : ( - \infty , \infty )$

Question 5

Solve the problem.
-The accompanying figure shows the graph of $y = x ^ { 2 }$ shifted to a new position. Write the equation for the new graph.

Accepted Answer

A)  $y = ( x - 6 ) ^ { 2 }$ 
B)  $y = ( x + 6 ) ^ { 2 }$ 
C)  $y = x ^ { 2 } - 6$ 
D)  $y = x ^ { 2 } + 6$ 
A)  $y = ( x - 6 ) ^ { 2 }$ 
B)  $y = ( x + 6 ) ^ { 2 }$ 
C)  $y = x ^ { 2 } - 6$ 
D)  $y = x ^ { 2 } + 6$

Question 6

Simplify the expression.
-$\log _ { 4 } \sqrt [ 3 ] { \frac { 1 } { 16 } }$

Accepted Answer

A)  $\frac { 2 } { 3 }$ 
B)  $\frac { 3 } { 2 }$ 
C)  $- \frac { 3 } { 2 }$ 
D)  $- \frac { 2 } { 3 }$ 
A)  $\frac { 2 } { 3 }$ 
B)  $\frac { 3 } { 2 }$ 
C)  $- \frac { 3 } { 2 }$ 
D)  $- \frac { 2 } { 3 }$

Question 7

Solve the problem.
-A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 11 inches by 27 inches by cutting out equal squares of side x at each corner and then folding up the sides as in the figure.
Express the volume V of the box as a function of x.

Accepted Answer

A)  $\mathrm { V } ( \mathrm { x } ) = \mathrm { x } ( 11 - 2 \mathrm { x } ) ( 27 - 2 \mathrm { x } )$ 
B)  $\mathrm { V } ( \mathrm { x } ) = ( 11 - 2 \mathrm { x } ) ( 27 - 2 \mathrm { x } )$ 
C)  $V ( x ) = ( 11 - x ) ( 27 - x )$ 
D)  $V ( x ) = x ( 11 - x ) ( 27 - x )$ 
A)  $\mathrm { V } ( \mathrm { x } ) = \mathrm { x } ( 11 - 2 \mathrm { x } ) ( 27 - 2 \mathrm { x } )$ 
B)  $\mathrm { V } ( \mathrm { x } ) = ( 11 - 2 \mathrm { x } ) ( 27 - 2 \mathrm { x } )$ 
C)  $V ( x ) = ( 11 - x ) ( 27 - x )$ 
D)  $V ( x ) = x ( 11 - x ) ( 27 - x )$

Question 8

Solve the problem.
-In the formula N $$\mathrm { N } = \mathrm { I } \mathrm { e } ^ { \mathrm { kt } }$$ N is the number of items in terms of an initial population I at a given time t and k is a growth constant equal to the percent of growth per unit time. There are currently 55 million cars in a certain
Country, increasing by 3.7% annually. How many years will it take for this country to have 75 million cars?
Round to the nearest year.

Accepted Answer

A)  5 yr 
B)  4 yr 
C)  81 yr 
D)  8 yr 
A)  5 yr 
B)  4 yr 
C)  81 yr 
D)  8 yr

Question 9

Solve the problem.
-The accompanying figure shows the graph of $y = - x ^ { 2 }$ shifted to a new position. Write the equation for the new graph.

Accepted Answer

A)  $y = - x ^ { 2 } - 2$ 
B)  $y = - ( x - 2 ) ^ { 2 }$ 
C)  $y = - ( x + 2 ) ^ { 2 }$ 
D)  $y = - x ^ { 2 } + 2$ 
A)  $y = - x ^ { 2 } - 2$ 
B)  $y = - ( x - 2 ) ^ { 2 }$ 
C)  $y = - ( x + 2 ) ^ { 2 }$ 
D)  $y = - x ^ { 2 } + 2$

Question 10

Graph the function.
-$g ( x ) = \left\{ \begin{array} { l l } 
- 3 & x \leq 0 \
x - 2 , & x > 0
\end{array} \right.$

Accepted Answer

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

Question 11

Provide an appropriate response.
-Graph the functions $f ( x ) = \frac { 3 } { x - 1 }$ and $g ( x ) = \frac { 2 } { x + 1 }$ together to identify the values of $x$ for which $\frac { 3 } { x - 1 } < \frac { 2 } { x + 1 }$. Confirm your findings algebraically.

Accepted Answer

A)  $( - \infty , - 5 )$ 
B)  $( - 5 , \infty )$ 
C)  $( - 1,1 ) \cup ( 1 , \infty )$ 
D)  $( - 5 , - 1 ) \cup ( 1 , \infty )$ 
A)  $( - \infty , - 5 )$ 
B)  $( - 5 , \infty )$ 
C)  $( - 1,1 ) \cup ( 1 , \infty )$ 
D)  $( - 5 , - 1 ) \cup ( 1 , \infty )$

Question 12

Graph the function in the ts-plane (t-axis horizontal, s-axis vertical). State the period and symmetry of the function.
-$s=\sec \left(\frac{t}{3}\right)$

Accepted Answer

A)  Period $6 \pi$, symmetric about the s-axis
  
B)  Period $6 \pi$, symmetric about the t-axis
  
C)  $\text { Period } 6 \pi \text {, symmetric about the } t \text {-axis }$
  
D) $\text { Period } 6 \pi \text {, symmetric about the } s \text {-axis }$
  
A)  Period $6 \pi$, symmetric about the s-axis
  
B)  Period $6 \pi$, symmetric about the t-axis
  
C)  $\text { Period } 6 \pi \text {, symmetric about the } t \text {-axis }$
  
D) $\text { Period } 6 \pi \text {, symmetric about the } s \text {-axis }$

Question 13

Determine if the function is even, odd, or neither.
-$$f ( x ) = - 3 x ^ { 4 } + 2 x - 8$$

Accepted Answer

A)  Even 
B)  Odd 
C)  Neither 
A)  Even 
B)  Odd 
C)  Neither

Question 14

Graph the function. Determine the symmetry, if any, of the function.
-$y=-|x|$

Accepted Answer

A)  Symmetric about the $x$-axis
  
B)  Symmetric about the $y$-axis
  
C)  Symmetric about the origin
  
D)  Symmetric about the $y$-axis
  
A)  Symmetric about the $x$-axis
  
B)  Symmetric about the $y$-axis
  
C)  Symmetric about the origin
  
D)  Symmetric about the $y$-axis

Question 15

State the domain and range of the function.
-$$f ( x ) = \sqrt { 25 + 8 ^ { - x } }$$

Accepted Answer

A)  domain: $( - \infty , \infty )$; range: $( 0,5 )$ 
B)  domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$ 
C)  domain: $( - \infty , \infty )$; range: $( 5 , \infty )$ 
D)  domain: $( 0 , \infty )$; range: $( - \infty , \infty )$ 
A)  domain: $( - \infty , \infty )$; range: $( 0,5 )$ 
B)  domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$ 
C)  domain: $( - \infty , \infty )$; range: $( 5 , \infty )$ 
D)  domain: $( 0 , \infty )$; range: $( - \infty , \infty )$

Question 16

For $$f ( x ) = A \sin \left( \frac { 2 \pi } { B } ( x - C ) \right) + D$$ identify either A, B, C, or D as ind icated for the sine function.
Find A.
-$$y = - 2 \sin \left( - \theta + \frac { \pi } { 2 } \right)$$

Accepted Answer

A)  $\frac { \pi } { 2 }$ 
B)  -4 
C)  - 1 
D)  - 2 
A)  $\frac { \pi } { 2 }$ 
B)  -4 
C)  - 1 
D)  - 2

Question 17

Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing.
-$y=-|x|$

Accepted Answer

A)

B)

C)  Increasing $- \infty < x < \infty$
  
D)  Increasing $- \infty < x \leq 0$
Decreasing $0 \leq \mathrm { x } < \infty$
  
A)

B)

C)  Increasing $- \infty < x < \infty$
  
D)  Increasing $- \infty < x \leq 0$
Decreasing $0 \leq \mathrm { x } < \infty$

Question 18

Provide an appropriate response.
-Consider a linear function that is perpendicular to the line $y = x$. Will this function be its own inverse? Explain.

Accepted Answer

A)  Yes it will be its own inverse. If it is perpendicular to $y = x$ it is symmetric with respect to $y = x$. Therefore it is its own inverse. 
B)  No it won't be its own inverse. Its inverse will be some other line that is perpendicular to it. 
C)  No it won't be its own inverse. The slope will be the same but the y-intercept will be different. 
D)  Yes it will be its own inverse. All perpendicular lines are their own inverses. 
A)  Yes it will be its own inverse. If it is perpendicular to $y = x$ it is symmetric with respect to $y = x$. Therefore it is its own inverse. 
B)  No it won't be its own inverse. Its inverse will be some other line that is perpendicular to it. 
C)  No it won't be its own inverse. The slope will be the same but the y-intercept will be different. 
D)  Yes it will be its own inverse. All perpendicular lines are their own inverses.

Question 19

Find the formula for the function.
-Express the area of a square as a function of its side length x.

Accepted Answer

A)  A = 4x 
B)  $A=x^{2}$ 
C)  A = 2x 
D)  $\mathrm{A}=\mathrm{x}^{4}$ 
A)  A = 4x 
B)  $A=x^{2}$ 
C)  A = 2x 
D)  $\mathrm{A}=\mathrm{x}^{4}$

Question 20

Find a formula for the function graphed.
-

Accepted Answer

A) $f ( x ) = \left\{ \begin{array} { l l } 5 x , & x \leq 0 \ - 5 x , & x > 0 \end{array} \right.$ B) $f ( x ) = \left\{ \begin{array} { l l } - 5 , & x \leq 0 \ 5 , & x > 0 \end{array} \right.$ C) $f ( x ) = \left\{ \begin{array} { l l } 5 , & x \leq 0 \ - 5 , & x > 0 \end{array} \right.$ D) $f ( x ) = \left\{ \begin{array} { l l } 5 , & x < 0 \ - 5 , & x \geq 0 \end{array} \right.$ A) $f ( x ) = \left\{ \begin{array} { l l } 5 x , & x \leq 0 \ - 5 x , & x > 0 \end{array} \right.$ B) $f ( x ) = \left\{ \begin{array} { l l } - 5 , & x \leq 0 \ 5 , & x > 0 \end{array} \right.$ C) $f ( x ) = \left\{ \begin{array} { l l } 5 , & x \leq 0 \ - 5 , & x > 0 \end{array} \right.$ D) $f ( x ) = \left\{ \begin{array} { l l } 5 , & x < 0 \ - 5 , & x \geq 0 \end{array} \right.$

Using the graph below, find the domain and range of the given function, and sketch the graph. - $y=f(-x)$

Solve the problem. - $\text { Use the angle sum formulas to derive } \sin ( A - B ) = \sin A \cos B - \cos A \sin B \text {. }$

Solve the problem. -Suppose the consumption of electricity grows at 5.8% per year, compounded continuously. Find the number of years before the use of electricity has tripled. Round the answer to the nearest hundredth.

Find the domain and range of the function. - $g ( z ) = \frac { - 5 } { \sqrt { z + 1 } }$

Solve the problem. -The accompanying figure shows the graph of $y = x ^ { 2 }$ shifted to a new position. Write the equation for the new graph. $Solve the problem. -The accompanying figure shows the graph of y = x ^ { 2 } shifted to a new position. Write the equation for the new graph.$

Simplify the expression. - $\log _ { 4 } \sqrt [ 3 ] { \frac { 1 } { 16 } }$

Solve the problem. -A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 11 inches by 27 inches by cutting out equal squares of side x at each corner and then folding up the sides as in the figure. Express the volume V of the box as a function of x.

Solve the problem. -The accompanying figure shows the graph of $y = - x ^ { 2 }$ shifted to a new position. Write the equation for the new graph. $Solve the problem. -The accompanying figure shows the graph of y = - x ^ { 2 } shifted to a new position. Write the equation for the new graph.$

Graph the function. - $g ( x ) = \left\{ \begin{array} { l l } - 3 & x \leq 0 \\x - 2 , & x > 0\end{array} \right.$ $Graph the function. - g ( x ) = \left\{ \begin{array} { l l } - 3 & x \leq 0 \\ x - 2 , & x > 0 \end{array} \right.$

Provide an appropriate response. -Graph the functions $f ( x ) = \frac { 3 } { x - 1 }$ and $g ( x ) = \frac { 2 } { x + 1 }$ together to identify the values of $x$ for which $\frac { 3 } { x - 1 } < \frac { 2 } { x + 1 }$ . Confirm your findings algebraically.

Determine if the function is even, odd, or neither. - $f ( x ) = - 3 x ^ { 4 } + 2 x - 8$

Graph the function. Determine the symmetry, if any, of the function. - $y=-|x|$

State the domain and range of the function. - $f ( x ) = \sqrt { 25 + 8 ^ { - x } }$

For $f ( x ) = A \sin \left( \frac { 2 \pi } { B } ( x - C ) \right) + D$ identify either A, B, C, or D as ind icated for the sine function. Find A. - $y = - 2 \sin \left( - \theta + \frac { \pi } { 2 } \right)$

Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - $y=-|x|$

Provide an appropriate response. -Consider a linear function that is perpendicular to the line $y = x$ . Will this function be its own inverse? Explain.

Find the formula for the function. -Express the area of a square as a function of its side length x.

Find a formula for the function graphed. -

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Exam 2: Functions

Using the graph below, find the domain and range of the given function, and sketch the graph. - y=f(−x)y=f(-x)y=f(−x)

Solve the problem. - Use the angle sum formulas to derive sin⁡(A−B)=sin⁡Acos⁡B−cos⁡Asin⁡B. \text { Use the angle sum formulas to derive } \sin ( A - B ) = \sin A \cos B - \cos A \sin B \text {. } Use the angle sum formulas to derive sin(A−B)=sinAcosB−cosAsinB.