Question 1

Solve the problem.
-Find the amount of interest earned on the following deposit: $1,000 at 9% compounded annually for 4 years

Accepted Answer

A)  $295.03 
B)  $538.62 
C)  $411.58 
D)  $1411.58 
A)  $295.03 
B)  $538.62 
C)  $411.58 
D)  $1411.58

Question 2

Graph the inverse of the function plotted, on the same set of axes. Use a dashed curve for the inverse.
-

Accepted Answer

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

Question 3

Using the graph below, find the domain and range of the given function, and sketch the graph.  
-$y=f(-x-2)+1$

Accepted Answer

A)  D: $[ - 7,2 ] ;$ R: $[ - 2,4 ]$
  
B)  D: $[ - 6,3 ] ; R : [ - 2,4 ]$
  
C)  D: $[ - 7,2 ] ; R : [ - 2,4 ]$
  
D)  D: $[ - 3,6 ] ; R : [ - 2,4 ]$
  
A)  D: $[ - 7,2 ] ;$ R: $[ - 2,4 ]$
  
B)  D: $[ - 6,3 ] ; R : [ - 2,4 ]$
  
C)  D: $[ - 7,2 ] ; R : [ - 2,4 ]$
  
D)  D: $[ - 3,6 ] ; R : [ - 2,4 ]$

Question 4

Find the domain and graph the function.
-f(x) = 8x + 4

Accepted Answer

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

Question 5

Solve the problem.
-A power plant is located on a river that is 650 feet wide. To lay a new cable from the plant to a location in a city 2 miles downstream on the opposite side costs $175 per foot across the river and $125 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)  $C ( x ) = 125 \sqrt { x ^ { 2 } + 650 ^ { 2 } } + 175 ( 10,560 - x )$ 
B)  $C ( x ) = 175 \sqrt { x ^ { 2 } + 650 ^ { 2 } } + 125 ( 10,560 - x )$ 
C)  $C ( x ) = 175 \sqrt { x ^ { 2 } + 650 ^ { 2 } } + 125 ( 2 - x )$ 
D)  $C ( x ) = 175 ( 650 - x ) + 125 ( 2 - x )$ 
A)  $C ( x ) = 125 \sqrt { x ^ { 2 } + 650 ^ { 2 } } + 175 ( 10,560 - x )$ 
B)  $C ( x ) = 175 \sqrt { x ^ { 2 } + 650 ^ { 2 } } + 125 ( 10,560 - x )$ 
C)  $C ( x ) = 175 \sqrt { x ^ { 2 } + 650 ^ { 2 } } + 125 ( 2 - x )$ 
D)  $C ( x ) = 175 ( 650 - x ) + 125 ( 2 - x )$

Question 6

Find the domain and range of the function.
-$\mathrm { F } ( \mathrm { t } ) = \frac { 7 } { 4 \sqrt { t } }$

Accepted Answer

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

Question 7

Use the appropriate addition formula to find the exact value of the expression.
-$\sin \left( \frac { 17 \pi } { 12 } \right)$

Accepted Answer

A)  $- \frac { \sqrt { 6 } + \sqrt { 2 } } { 4 }$ 
B)  $\frac { \sqrt { 6 } + \sqrt { 2 } } { 4 }$ 
C)  $\frac { \sqrt { 2 } - \sqrt { 6 } } { 4 }$ 
D)  $\frac { \sqrt { 6 } - \sqrt { 2 } } { 4 }$ 
A)  $- \frac { \sqrt { 6 } + \sqrt { 2 } } { 4 }$ 
B)  $\frac { \sqrt { 6 } + \sqrt { 2 } } { 4 }$ 
C)  $\frac { \sqrt { 2 } - \sqrt { 6 } } { 4 }$ 
D)  $\frac { \sqrt { 6 } - \sqrt { 2 } } { 4 }$

Question 8

Graph the function. Determine the symmetry, if any, of the function.
-$y=-x^{4 / 5}$

Accepted Answer

A)  No symmetry
  
B)  Symmetric about the $y$-axis
  
C)  Symmetric about the $y$-axis
  
D)  No symmetry
  
A)  No symmetry
  
B)  Symmetric about the $y$-axis
  
C)  Symmetric about the $y$-axis
  
D)  No symmetry

Question 9

Solve for t or y, as appropriate.
-$$e ^ { x ^ { 2 } } e ^ { 3 x + 2 } = e ^ { t }$$

Accepted Answer

A)  $x ^ { 2 } - 3 x - 2$ 
B)  $x ^ { 2 } + 3 x + 2$ 
C)  $3 x ^ { 3 } + 2 x ^ { 2 }$ 
D)  $\ln \left( x ^ { 2 } + 3 x + 2 \right)$ 
A)  $x ^ { 2 } - 3 x - 2$ 
B)  $x ^ { 2 } + 3 x + 2$ 
C)  $3 x ^ { 3 } + 2 x ^ { 2 }$ 
D)  $\ln \left( x ^ { 2 } + 3 x + 2 \right)$

Question 10

Graph the function.
-$f ( x ) = \left\{ \begin{array} { l l } 
4 x + 2 , & x  3
\end{array} \right.$

Accepted Answer

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

Question 11

Find the domain and graph the function.
-$G(x)=\sqrt{|x|}$

Accepted Answer

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

Question 12

Find the domain and range of the function.
-$f ( x ) = - 4 + \sqrt { x }$

Accepted Answer

A)  D: $( - \infty , \infty )$, R: $[ - 4 , \infty )$ 
B)  D: $[ 0 , \infty )$, R: $[ - 4 , \infty )$ 
C)  D: $[ 0 , \infty )$, R: $( - \infty , \infty )$ 
D)  D: $( - \infty , 0 ] , R : ( - \infty , - 4 ]$ 
A)  D: $( - \infty , \infty )$, R: $[ - 4 , \infty )$ 
B)  D: $[ 0 , \infty )$, R: $[ - 4 , \infty )$ 
C)  D: $[ 0 , \infty )$, R: $( - \infty , \infty )$ 
D)  D: $( - \infty , 0 ] , R : ( - \infty , - 4 ]$

Question 13

Solve for t or y, as appropriate.
-$$\mathrm { e } ^ { 2 \mathrm { t } } = 49$$

Accepted Answer

A)  $\frac { e ^ { 49 } } { 2 }$ 
B)  $\ln 7$ 
C)  $\ln 49$ 
D)  $\ln \frac { 49 } { 2 }$ 
A)  $\frac { e ^ { 49 } } { 2 }$ 
B)  $\ln 7$ 
C)  $\ln 49$ 
D)  $\ln \frac { 49 } { 2 }$

Question 14

Solve the problem.
-Let $g ( x ) = x + 6$. Find a function $y = f ( x )$ so that $( f \circ g ) ( x ) = 4 x + 24$

Accepted Answer

A)  $f ( x ) = 4 x$ 
B)  $f ( x ) = 4 x + 6$ 
C)  $f ( x ) = 4 x - 6$ 
D)  $f ( x ) = 4 ( x + 1 )$ 
A)  $f ( x ) = 4 x$ 
B)  $f ( x ) = 4 x + 6$ 
C)  $f ( x ) = 4 x - 6$ 
D)  $f ( x ) = 4 ( x + 1 )$

Question 15

Determine an appropriate viewing window for the given function and use it to display its graph.
-$f ( x ) = \frac { 18 x } { x ^ { 2 } - 9 }$

Accepted Answer

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

Question 16

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)  $y = x ^ { 2 } + 4$ 
B)  $y = x ^ { 2 } - 4$ 
C)  $y = ( x - 4 ) ^ { 2 }$ 
D)  $y = ( x + 4 ) ^ { 2 }$ 
A)  $y = x ^ { 2 } + 4$ 
B)  $y = x ^ { 2 } - 4$ 
C)  $y = ( x - 4 ) ^ { 2 }$ 
D)  $y = ( x + 4 ) ^ { 2 }$

Question 17

Determine whether or not the graph is a graph of a function of x.
-

Accepted Answer

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

Question 18

Consider the function y Can x be 0?
-Graph the equation |y| = x and decide whether or not the graph represents a function of x.

Accepted Answer

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

Question 19

Graph the inverse of the function plotted, on the same set of axes. Use a dashed curve for the inverse.
-

Accepted Answer

A) 
  
B) 
  
C) 
  
D)  Function is its own inverse.
  
A) 
  
B) 
  
C) 
  
D)  Function is its own inverse.

Question 20

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

Accepted Answer

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

Solve the problem. -Find the amount of interest earned on the following deposit: $1,000 at 9% compounded annually for 4 years

Graph the inverse of the function plotted, on the same set of axes. Use a dashed curve for the inverse. -

Using the graph below, find the domain and range of the given function, and sketch the graph. - $y=f(-x-2)+1$

Find the domain and graph the function. -f(x) = 8x + 4

Find the domain and range of the function. - $\mathrm { F } ( \mathrm { t } ) = \frac { 7 } { 4 \sqrt { t } }$

Use the appropriate addition formula to find the exact value of the expression. - $\sin \left( \frac { 17 \pi } { 12 } \right)$

Graph the function. Determine the symmetry, if any, of the function. - $y=-x^{4 / 5}$ $Graph the function. Determine the symmetry, if any, of the function. - y=-x^{4 / 5}$

Solve for t or y, as appropriate. - $e ^ { x ^ { 2 } } e ^ { 3 x + 2 } = e ^ { t }$

Graph the function. - $f ( x ) = \left\{ \begin{array} { l l } 4 x + 2 , & x < - 2 \\x , & - 2 \leq x \leq 3 \\3 x - 1 , & x > 3\end{array} \right.$ $Graph the function. - f ( x ) = \left\{ \begin{array} { l l } 4 x + 2 , & x < - 2 \\ x , & - 2 \leq x \leq 3 \\ 3 x - 1 , & x > 3 \end{array} \right.$

Find the domain and graph the function. - $G(x)=\sqrt{|x|}$ $Find the domain and graph the function. - G(x)=\sqrt{|x|}$

Find the domain and range of the function. - $f ( x ) = - 4 + \sqrt { x }$

Solve for t or y, as appropriate. - $\mathrm { e } ^ { 2 \mathrm { t } } = 49$

Solve the problem. -Let $g ( x ) = x + 6$ . Find a function $y = f ( x )$ so that $( f \circ g ) ( x ) = 4 x + 24$

Determine an appropriate viewing window for the given function and use it to display its graph. - $f ( x ) = \frac { 18 x } { x ^ { 2 } - 9 }$ $Determine an appropriate viewing window for the given function and use it to display its graph. - f ( x ) = \frac { 18 x } { x ^ { 2 } - 9 }$

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

Determine whether or not the graph is a graph of a function of x. -

Consider the function y Can x be 0? -Graph the equation |y| = x and decide whether or not the graph represents a function of x.

Graph the inverse of the function plotted, on the same set of axes. Use a dashed curve for the inverse. -

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

Limits and Continuity

Derivatives

Applications of Derivatives

Integrals

Applications of Definite Integrals

Integrals and Transcendental Functions

Techniques of Integration

First-Order Differential Equations

Infinite Sequences and Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions and Motion in Space

Partial Derivatives

Multiple Integrals

Integrals and Vector Fields

Filters

Exam 2: Functions

Solve the problem. -Find the amount of interest earned on the following deposit: $1,000 at 9% compounded annually for 4 years

Graph the inverse of the function plotted, on the same set of axes. Use a dashed curve for the inverse. -

Using the graph below, find the domain and range of the given function, and sketch the graph. - y=f(−x−2)+1y=f(-x-2)+1y=f(−x−2)+1

Find the domain and graph the function. -f(x) = 8x + 4

Find the domain and range of the function. - F(t)=74t\mathrm { F } ( \mathrm { t } ) = \frac { 7 } { 4 \sqrt { t } }F(t)=4t​7​

Use the appropriate addition formula to find the exact value of the expression. - sin⁡(17π12)\sin \left( \frac { 17 \pi } { 12 } \right)sin(1217π​)

Graph the function. Determine the symmetry, if any, of the function. - y=−x4/5y=-x^{4 / 5}y=−x4/5

Solve for t or y, as appropriate. - ex2e3x+2=ete ^ { x ^ { 2 } } e ^ { 3 x + 2 } = e ^ { t }ex2e3x+2=et

Graph the function. - f(x)={4x+2,x<−2x,−2≤x≤33x−1,x>3f ( x ) = \left\{ \begin{array} { l l } 4 x + 2 , & x < - 2 \\x , & - 2 \leq x \leq 3 \\3 x - 1 , & x > 3\end{array} \right.f(x)=⎩⎨⎧​4x+2,x,3x−1,​x<−2−2≤x≤3x>3​

Find the domain and graph the function. - G(x)=∣x∣G(x)=\sqrt{|x|}G(x)=∣x∣​

Find the domain and range of the function. - f(x)=−4+xf ( x ) = - 4 + \sqrt { x }f(x)=−4+x​

Solve for t or y, as appropriate. - e2t=49\mathrm { e } ^ { 2 \mathrm { t } } = 49e2t=49

Solve the problem. -Let g(x)=x+6g ( x ) = x + 6g(x)=x+6 . Find a function y=f(x)y = f ( x )y=f(x) so that (f∘g)(x)=4x+24( f \circ g ) ( x ) = 4 x + 24(f∘g)(x)=4x+24

Determine an appropriate viewing window for the given function and use it to display its graph. - f(x)=18xx2−9f ( x ) = \frac { 18 x } { x ^ { 2 } - 9 }f(x)=x2−918x​

Solve the problem. -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 whether or not the graph is a graph of a function of x. -

Consider the function y Can x be 0? -Graph the equation |y| = x and decide whether or not the graph represents a function of x.

Graph the inverse of the function plotted, on the same set of axes. Use a dashed curve for the inverse. -

Determine if the function is even, odd, or neither. - f(x)=2x2+2f ( x ) = \frac { 2 } { x ^ { 2 } + 2 }f(x)=x2+22​

Limits and Continuity

Derivatives

Applications of Derivatives

Integrals

Applications of Definite Integrals

Integrals and Transcendental Functions

Techniques of Integration

First-Order Differential Equations

Infinite Sequences and Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions and Motion in Space

Partial Derivatives

Multiple Integrals

Integrals and Vector Fields

Filters

Using the graph below, find the domain and range of the given function, and sketch the graph. - $y=f(-x-2)+1$

Find the domain and range of the function. - $\mathrm { F } ( \mathrm { t } ) = \frac { 7 } { 4 \sqrt { t } }$

Use the appropriate addition formula to find the exact value of the expression. - $\sin \left( \frac { 17 \pi } { 12 } \right)$

Graph the function. Determine the symmetry, if any, of the function. - $y=-x^{4 / 5}$ $Graph the function. Determine the symmetry, if any, of the function. - y=-x^{4 / 5}$

Solve for t or y, as appropriate. - $e ^ { x ^ { 2 } } e ^ { 3 x + 2 } = e ^ { t }$

Find the domain and graph the function. - $G(x)=\sqrt{|x|}$ $Find the domain and graph the function. - G(x)=\sqrt{|x|}$

Find the domain and range of the function. - $f ( x ) = - 4 + \sqrt { x }$

Solve for t or y, as appropriate. - $\mathrm { e } ^ { 2 \mathrm { t } } = 49$

Solve the problem. -Let $g ( x ) = x + 6$ . Find a function $y = f ( x )$ so that $( f \circ g ) ( x ) = 4 x + 24$

Determine an appropriate viewing window for the given function and use it to display its graph. - $f ( x ) = \frac { 18 x } { x ^ { 2 } - 9 }$ $Determine an appropriate viewing window for the given function and use it to display its graph. - f ( x ) = \frac { 18 x } { x ^ { 2 } - 9 }$

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

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