Question 1

Find a formula for the function graphed.
-

Accepted Answer

A)  $f ( x ) = \left\{ \begin{array} { l l } 2 , & 0 \leq x < 6 \ 6 , & 2 \leq x < 8 \end{array} \right.$ 
B)  $f ( x ) = \left\{ \begin{array} { l l } 6 , & 0 \leq x < 6 \ 2 , & 2 \leq x < 8 \end{array} \right.$ 
C)  $f ( x ) = \left\{ \begin{array} { l l } 2 , & 0 \leq x \leq 2 \ 6 , & 2 < x \leq 4 \ 2 , & 4 < x \leq 6 \ 6 , & 6 < x \leq 8 \end{array} \right.$ 
D)  $f ( x ) = \left\{ \begin{array} { l l } 2 , & 0 \leq x < 2 \ 6 , & 2 \leq x < 4 \ 2 , & 4 \leq x < 6 \ 6 , & 6 \leq x < 8 \end{array} \right.$ 
A)  $f ( x ) = \left\{ \begin{array} { l l } 2 , & 0 \leq x < 6 \ 6 , & 2 \leq x < 8 \end{array} \right.$ 
B)  $f ( x ) = \left\{ \begin{array} { l l } 6 , & 0 \leq x < 6 \ 2 , & 2 \leq x < 8 \end{array} \right.$ 
C)  $f ( x ) = \left\{ \begin{array} { l l } 2 , & 0 \leq x \leq 2 \ 6 , & 2 < x \leq 4 \ 2 , & 4 < x \leq 6 \ 6 , & 6 < x \leq 8 \end{array} \right.$ 
D)  $f ( x ) = \left\{ \begin{array} { l l } 2 , & 0 \leq x < 2 \ 6 , & 2 \leq x < 4 \ 2 , & 4 \leq x < 6 \ 6 , & 6 \leq x < 8 \end{array} \right.$

Question 2

Provide an appropriate response.
-$\text { Consider the function } y = \sqrt { 1 - \frac { 1 } { x } } \text {. Can } x \text { be negative? }$

Accepted Answer

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

Question 3

Express the given function as a composite of functions f and g such that y = f(g(x)).
-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)  $y = x ^ { 2 } - 5$ 
B)  $y = ( x + 5 ) ^ { 2 }$ 
C)  $y = x ^ { 2 } + 5$ 
D)  $y = ( x - 5 ) ^ { 2 }$ 
A)  $y = x ^ { 2 } - 5$ 
B)  $y = ( x + 5 ) ^ { 2 }$ 
C)  $y = x ^ { 2 } + 5$ 
D)  $y = ( x - 5 ) ^ { 2 }$

Question 4

A power plant is located on a river that is 600 feet wide. To lay a new cable from the plant to a location in a city 2 miles downstream on the opposite side costs $225 per foot across the river and $150 per foot along the land.
Suppose that the cable goes from the plant to a point Q on the opposite side that is x feet from the point P
Directly opposite the plant. Write a function C(x) that gives the cost of laying the cable in terms of the distance x.

Accepted Answer

A)  $C ( x ) = 225 \sqrt { x ^ { 2 } + 600 ^ { 2 } } + 150 ( 2 - x )$ 
B)  $C ( x ) = 225 ( 600 - x ) + 150 ( 2 - x )$ 
C)  $C ( x ) = 150 \sqrt { x ^ { 2 } + 600 ^ { 2 } } + 225 ( 10,560 - x )$ 
D)  $C ( x ) = 225 \sqrt { x ^ { 2 } + 600 ^ { 2 } } + 150 ( 10,560 - x )$ 
A)  $C ( x ) = 225 \sqrt { x ^ { 2 } + 600 ^ { 2 } } + 150 ( 2 - x )$ 
B)  $C ( x ) = 225 ( 600 - x ) + 150 ( 2 - x )$ 
C)  $C ( x ) = 150 \sqrt { x ^ { 2 } + 600 ^ { 2 } } + 225 ( 10,560 - x )$ 
D)  $C ( x ) = 225 \sqrt { x ^ { 2 } + 600 ^ { 2 } } + 150 ( 10,560 - x )$

Question 5

Determine if the function is even, odd, or neither.
-$y = 5 x$

Accepted Answer

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

Question 6

Find a formula for the function graphed.
-

Accepted Answer

A)  $f ( x ) = \left\{ \begin{array} { l l } 4 , & x  0 \end{array} \right.$ 
C)  $f ( x ) = \left\{ \begin{array} { l l } 4 , & x < 0 \ - x , & x \geq 0 \end{array} \right.$ 
D)  $f ( x ) = \left\{ \begin{array} { l l } 4 , & x < 0 \ - 4 x , & x \geq 0 \end{array} \right.$ 
A)  $f ( x ) = \left\{ \begin{array} { l l } 4 , & x  0 \end{array} \right.$ 
C)  $f ( x ) = \left\{ \begin{array} { l l } 4 , & x < 0 \ - x , & x \geq 0 \end{array} \right.$ 
D)  $f ( x ) = \left\{ \begin{array} { l l } 4 , & x < 0 \ - 4 x , & x \geq 0 \end{array} \right.$

Question 7

Provide an appropriate response.
-Graph the functions $f ( x ) = \frac { 4 } { x - 1 }$ and $g ( x ) = \frac { 2 } { x + 1 }$ together to identify the values of $x$ for which $\frac { 4 } { x - 1 } < \frac { 2 } { x + 1 }$. Confirm your findings algebraically.

Accepted Answer

A)  $( - 1,1 ) \cup ( 1 , \infty )$ 
B)  $( - 3 , - 1 ) \cup ( 1 , \infty )$ 
C)  $( - 3 , \infty )$ 
D)  $( - \infty , - 3 )$ 
A)  $( - 1,1 ) \cup ( 1 , \infty )$ 
B)  $( - 3 , - 1 ) \cup ( 1 , \infty )$ 
C)  $( - 3 , \infty )$ 
D)  $( - \infty , - 3 )$

Question 8

Find the domain and range for the indicated function.
-If f(x) = -2x + 3 and g(x) = 5x + 5, find g(f(x)).

Accepted Answer

A)  10x + 20 
B)  -10x - 10 
C)  -10x + 20 
D)  -10x + 13 
A)  10x + 20 
B)  -10x - 10 
C)  -10x + 20 
D)  -10x + 13

Question 9

Find the domain and range for the indicated function.
-$f ( x ) = 7 , \quad g ( x ) = 7 + \sqrt { x }$
$\mathrm { g } / \mathrm { f }$

Accepted Answer

A)  D: $x \geq 0$
R: $y \leq 7$ 
B)  D: $x \geq - 7$
R: $y \geq 0$ 
C)  D: $x \geq 0$
R: $y \geq 1$ 
D)  D: $x \geq 0$
R: $y \leq 1$ 
A)  D: $x \geq 0$
R: $y \leq 7$ 
B)  D: $x \geq - 7$
R: $y \geq 0$ 
C)  D: $x \geq 0$
R: $y \geq 1$ 
D)  D: $x \geq 0$
R: $y \leq 1$

Question 10

Provide an appropriate response.
-$\text { Graph the equation } | x + y | = 1 \text { and decide whether or not the graph represents a function of } x \text {. }$

Accepted Answer

A)  Function 
B)  Not a Function 
A)  Function 
B)  Not a Function

Question 11

Determine if the function is even, odd, or neither.
-$y = 3 ^ { x }$

Accepted Answer

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

Question 12

Find a formula for the function graphed.
-

Accepted Answer

A)  $f ( x ) = \left\{ \begin{array} { l l } - \frac { 1 } { 2 } x + 1 , & - 8 \leq x \leq - 2 \ 5 , & - 2 < x \leq 3 \ x - 6 , & 3 < x \leq 8 \end{array} \quad \right.$ 
B)  $f ( x ) = \left\{ \begin{array} { l l } \frac { 1 } { 2 } x + 1 , & - 8 < x \leq - 2 \ 5 , & - 2 < x \leq 3 \ 6 - x , & 3 < x < 8 \end{array} \right.$ 
C)  $f ( x ) = \left\{ \begin{array} { l l } \frac { 1 } { 2 } x + 1 , & - 8 \leq x \leq - 2 \ 5 , & - 2 < x < 3 \ 6 - x , & 3 \leq x \leq 8 \end{array} \right.$ 
D)  $f ( x ) = \left\{ \begin{array} { l r } \frac { 1 } { 2 } x + 1 , & - 8 \leq x \leq - 2 \ 5 , & - 2 < x \leq 3 \ 6 - x , & 3 < x \leq 8 \end{array} \right.$ 
A)  $f ( x ) = \left\{ \begin{array} { l l } - \frac { 1 } { 2 } x + 1 , & - 8 \leq x \leq - 2 \ 5 , & - 2 < x \leq 3 \ x - 6 , & 3 < x \leq 8 \end{array} \quad \right.$ 
B)  $f ( x ) = \left\{ \begin{array} { l l } \frac { 1 } { 2 } x + 1 , & - 8 < x \leq - 2 \ 5 , & - 2 < x \leq 3 \ 6 - x , & 3 < x < 8 \end{array} \right.$ 
C)  $f ( x ) = \left\{ \begin{array} { l l } \frac { 1 } { 2 } x + 1 , & - 8 \leq x \leq - 2 \ 5 , & - 2 < x < 3 \ 6 - x , & 3 \leq x \leq 8 \end{array} \right.$ 
D)  $f ( x ) = \left\{ \begin{array} { l r } \frac { 1 } { 2 } x + 1 , & - 8 \leq x \leq - 2 \ 5 , & - 2 < x \leq 3 \ 6 - x , & 3 < x \leq 8 \end{array} \right.$

Question 13

Find the formula for the function.
-Express the volume of a sphere as a function of its radius r.

Accepted Answer

A)  $V = \frac { 2 } { 3 } \pi r ^ { 2 }$ 
B)  $V = \frac { 3 } { 4 } \pi r ^ { 3 }$ 
C)  $\mathrm { V } = \frac { 4 } { 3 } \pi \mathrm { r } ^ { 3 }$ 
D)  $V = \pi r ^ { 3 }$ 
A)  $V = \frac { 2 } { 3 } \pi r ^ { 2 }$ 
B)  $V = \frac { 3 } { 4 } \pi r ^ { 3 }$ 
C)  $\mathrm { V } = \frac { 4 } { 3 } \pi \mathrm { r } ^ { 3 }$ 
D)  $V = \pi r ^ { 3 }$

Question 14

Find the domain and range of the function.
-$$F ( t ) = \frac { 10 } { 9 \sqrt { t } }$$

Accepted Answer

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

Question 15

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

Question 16

Find a formula for the function graphed.
-

Accepted Answer

A)  $f ( x ) = \left\{ \begin{array} { l l } 6 - x , & 0 \leq x \leq 3 \ x , & 3 < x \leq 6 \end{array} \right.$ 
B)  $f ( x ) = \left\{ \begin{array} { l l } x + 6 , & 0 \leq x \leq 3 \ - x , & 3 < x \leq 6 \end{array} \right.$ 
C)  $f ( x ) = \left\{ \begin{array} { l l } x , & 0 \leq x \leq 3 \ 6 - x , & 3 < x \leq 6 \end{array} \right.$ 
D)  $f ( x ) = \left\{ \begin{array} { l l } - x , & 0 \leq x \leq 3 \ x + 6 , & 3 < x \leq 6 \end{array} \right.$ 
A)  $f ( x ) = \left\{ \begin{array} { l l } 6 - x , & 0 \leq x \leq 3 \ x , & 3 < x \leq 6 \end{array} \right.$ 
B)  $f ( x ) = \left\{ \begin{array} { l l } x + 6 , & 0 \leq x \leq 3 \ - x , & 3 < x \leq 6 \end{array} \right.$ 
C)  $f ( x ) = \left\{ \begin{array} { l l } x , & 0 \leq x \leq 3 \ 6 - x , & 3 < x \leq 6 \end{array} \right.$ 
D)  $f ( x ) = \left\{ \begin{array} { l l } - x , & 0 \leq x \leq 3 \ x + 6 , & 3 < x \leq 6 \end{array} \right.$

Question 17

Find the domain and range for the indicated function.
-If $f ( x ) = 4 x + 7$ and $g ( x ) = - 7 x ^ { 2 } + 5 x + 2$, find $g ( f ( 4 ) )$.

Accepted Answer

A)  $- 44$ 
B)  $- 3586$ 
C)  $- 353$ 
D)  $- 17$ 
A)  $- 44$ 
B)  $- 3586$ 
C)  $- 353$ 
D)  $- 17$

Question 18

Find a formula for the function graphed.
-

Accepted Answer

A)  $f ( x ) = \left\{ \begin{array} { l l } - 2 x , & x \leq 1 \ x + 1 , & x > 1 \end{array} \right.$ 
B)  $f ( x ) = \left\{ \begin{array} { l l } - 2 x , & x \leq 1 \ x + 2 , & x > 1 \end{array} \right.$ 
C)  $f ( x ) = \left\{ \begin{array} { l l } 2 x , & x \leq 1 \ x + 1 , & x > 1 \end{array} \right.$ 
D)  $f ( x ) = \left\{ \begin{array} { l l } x , & x \leq 1 \ 2 x + 1 , & x > 1 \end{array} \right.$ 
A)  $f ( x ) = \left\{ \begin{array} { l l } - 2 x , & x \leq 1 \ x + 1 , & x > 1 \end{array} \right.$ 
B)  $f ( x ) = \left\{ \begin{array} { l l } - 2 x , & x \leq 1 \ x + 2 , & x > 1 \end{array} \right.$ 
C)  $f ( x ) = \left\{ \begin{array} { l l } 2 x , & x \leq 1 \ x + 1 , & x > 1 \end{array} \right.$ 
D)  $f ( x ) = \left\{ \begin{array} { l l } x , & x \leq 1 \ 2 x + 1 , & x > 1 \end{array} \right.$

Question 19

Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing.
-$y = - \frac { 1 } { x ^ { 2 } }$

Accepted Answer

A)  Increasing $- \infty < x < 0$ and $0 < x < \infty$
  
B)  Decreasing $- \infty < x < 0$
 Increasing $0< x < \infty $
  
C)  Decreasing $- \infty < x < 0$ and $0 < x < \infty$
  
D)  Increasing $- \infty < x < 0$
Decreasing $0< x < \infty $ 
  
A)  Increasing $- \infty < x < 0$ and $0 < x < \infty$
  
B)  Decreasing $- \infty < x < 0$
 Increasing $0< x < \infty $
  
C)  Decreasing $- \infty < x < 0$ and $0 < x < \infty$
  
D)  Increasing $- \infty < x < 0$
Decreasing $0< x < \infty $

Question 20

Provide an appropriate response.
-$\text { Graph the function } f ( x ) = \lceil x \rceil \text {. }$

Accepted Answer

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

Find a formula for the function graphed. -

Provide an appropriate response. - $\text { Consider the function } y = \sqrt { 1 - \frac { 1 } { x } } \text {. Can } x \text { be negative? }$

Determine if the function is even, odd, or neither. - $y = 5 x$

Find a formula for the function graphed. -

Provide an appropriate response. -Graph the functions $f ( x ) = \frac { 4 } { x - 1 }$ and $g ( x ) = \frac { 2 } { x + 1 }$ together to identify the values of $x$ for which $\frac { 4 } { x - 1 } < \frac { 2 } { x + 1 }$ . Confirm your findings algebraically.

Find the domain and range for the indicated function. -If f(x) = -2x + 3 and g(x) = 5x + 5, find g(f(x)).

Find the domain and range for the indicated function. - $f ( x ) = 7 , \quad g ( x ) = 7 + \sqrt { x }$ $\mathrm { g } / \mathrm { f }$

Determine if the function is even, odd, or neither. - $y = 3 ^ { x }$

Find a formula for the function graphed. -

Find the formula for the function. -Express the volume of a sphere as a function of its radius r.

Find the domain and range of the function. - $F ( t ) = \frac { 10 } { 9 \sqrt { t } }$

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

Find a formula for the function graphed. -

Find the domain and range for the indicated function. -If $f ( x ) = 4 x + 7$ and $g ( x ) = - 7 x ^ { 2 } + 5 x + 2$ , find $g ( f ( 4 ) )$ .

Find a formula for the function graphed. -

Provide an appropriate response. - $\text { Graph the function } f ( x ) = \lceil x \rceil \text {. }$ $Provide an appropriate response. - \text { Graph the function } f ( x ) = \lceil x \rceil \text {. }$

Limits and Derivatives

Differentiation

Applications of Derivatives

Integration

Applications of Definite Integrals

Integrals and Transcendental Functions

Techniques of Integration

First-Order Differential Equations

Infinite Sequences and Series

Filters

Exam 1: Functions

Find a formula for the function graphed. -

Provide an appropriate response. - Consider the function y=1−1x. Can x be negative? \text { Consider the function } y = \sqrt { 1 - \frac { 1 } { x } } \text {. Can } x \text { be negative? } Consider the function y=1−x1​​. Can x be negative?

Express the given function as a composite of functions f and g such that y = f(g(x)). -The accompanying figure shows the graph of y=x2y = x ^ { 2 }y=x2 shifted to a new position. Write the equation for the new graph.

Determine if the function is even, odd, or neither. - y=5xy = 5 xy=5x

Find a formula for the function graphed. -

Find the domain and range for the indicated function. -If f(x) = -2x + 3 and g(x) = 5x + 5, find g(f(x)).

Find the domain and range for the indicated function. - f(x)=7,g(x)=7+xf ( x ) = 7 , \quad g ( x ) = 7 + \sqrt { x }f(x)=7,g(x)=7+x​ g/f\mathrm { g } / \mathrm { f }g/f

Determine if the function is even, odd, or neither. - y=3xy = 3 ^ { x }y=3x

Find a formula for the function graphed. -

Find the formula for the function. -Express the volume of a sphere as a function of its radius r.

Find the domain and range of the function. - F(t)=109tF ( t ) = \frac { 10 } { 9 \sqrt { t } }F(t)=9t​10​

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

Find a formula for the function graphed. -

Find the domain and range for the indicated function. -If f(x)=4x+7f ( x ) = 4 x + 7f(x)=4x+7 and g(x)=−7x2+5x+2g ( x ) = - 7 x ^ { 2 } + 5 x + 2g(x)=−7x2+5x+2 , find g(f(4))g ( f ( 4 ) )g(f(4)) .

Find a formula for the function graphed. -

Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - y=−1x2y = - \frac { 1 } { x ^ { 2 } }y=−x21​

Provide an appropriate response. - Graph the function f(x)=⌈x⌉. \text { Graph the function } f ( x ) = \lceil x \rceil \text {. } Graph the function f(x)=⌈x⌉.

Limits and Derivatives

Differentiation

Applications of Derivatives

Integration

Applications of Definite Integrals

Integrals and Transcendental Functions

Techniques of Integration

First-Order Differential Equations

Infinite Sequences and Series

Filters

Provide an appropriate response. - $\text { Consider the function } y = \sqrt { 1 - \frac { 1 } { x } } \text {. Can } x \text { be negative? }$

Determine if the function is even, odd, or neither. - $y = 5 x$

Find the domain and range for the indicated function. - $f ( x ) = 7 , \quad g ( x ) = 7 + \sqrt { x }$ $\mathrm { g } / \mathrm { f }$

Determine if the function is even, odd, or neither. - $y = 3 ^ { x }$

Find the domain and range of the function. - $F ( t ) = \frac { 10 } { 9 \sqrt { t } }$

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

Find the domain and range for the indicated function. -If $f ( x ) = 4 x + 7$ and $g ( x ) = - 7 x ^ { 2 } + 5 x + 2$ , find $g ( f ( 4 ) )$ .

Provide an appropriate response. - $\text { Graph the function } f ( x ) = \lceil x \rceil \text {. }$ $Provide an appropriate response. - \text { Graph the function } f ( x ) = \lceil x \rceil \text {. }$