Question 1

Consider the function y Can x be 0?
-$$y = \sqrt { 1 - \frac { 1 } { x } }$$

Accepted Answer

A) True 
 B)False

Question 2

Find the domain and range of the function.
-$\mathrm { F } ( \mathrm { t } ) = \mathrm { t } ^ { 2 } - 8$

Accepted Answer

A)  D: $( - \infty , \infty )$, R: $( - \infty , \infty )$ 
B)  D: $( - \infty , \infty )$, R: $[ - 8 , \infty )$ 
C)  D: $[ 0 , \infty ) , R : ( - \infty , - 8 ]$ 
D)  D: $[ - 64 , \infty )$, R: $[ - 8 , \infty )$ 
A)  D: $( - \infty , \infty )$, R: $( - \infty , \infty )$ 
B)  D: $( - \infty , \infty )$, R: $[ - 8 , \infty )$ 
C)  D: $[ 0 , \infty ) , R : ( - \infty , - 8 ]$ 
D)  D: $[ - 64 , \infty )$, R: $[ - 8 , \infty )$

Question 3

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

Accepted Answer

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

Question 4

The problem tells how many units and in what direction the graph of the given equation is to be shifted. Give an
equation for the shifted graph. Then sketch the original graph with a dashed line and the shifted graph with a solid line.
-$y = - \sqrt { x }$
Left 6

Accepted Answer

A)  $y = \sqrt { x } + 6$
  
B)  $y = \sqrt { x - 6 }$
  
C)  $y=\sqrt{x}-6$
  
D)  $y=\sqrt{x+6}$
  
A)  $y = \sqrt { x } + 6$
  
B)  $y = \sqrt { x - 6 }$
  
C)  $y=\sqrt{x}-6$
  
D)  $y=\sqrt{x+6}$

Question 5

Find the exact function value.
-$\cos ^ { - 1 } \left( \frac { \sqrt { 2 } } { 2 } \right)$

Accepted Answer

A)  $\frac { \pi } { 4 }$ 
B)  $\frac { 11 \pi } { 6 }$ 
C)  $\frac { 7 \pi } { 4 }$ 
D)  $\frac { \pi } { 6 }$ 
A)  $\frac { \pi } { 4 }$ 
B)  $\frac { 11 \pi } { 6 }$ 
C)  $\frac { 7 \pi } { 4 }$ 
D)  $\frac { \pi } { 6 }$

Question 6

Use a graphing calculator or computer to determine which of the given viewing windows displays the most appropriate
graph of the specified function.
-$$f ( x ) = x ^ { 2 / 3 } ( 4 - x )$$

Accepted Answer

A)  $[ - 2,2 ]$ by $[ - 15,15 ]$ 
B)  $[ - 4,0 ]$ by $[ - 5,5 ]$ 
C)  $[ - 4,7 ]$ by $[ - 10,10 ]$ 
D)  $[ 0,7 ]$ by $[ - 10,10 ]$ 
A)  $[ - 2,2 ]$ by $[ - 15,15 ]$ 
B)  $[ - 4,0 ]$ by $[ - 5,5 ]$ 
C)  $[ - 4,7 ]$ by $[ - 10,10 ]$ 
D)  $[ 0,7 ]$ by $[ - 10,10 ]$

Question 7

Find the exact value of the trigonometric function. Do not use a calculator or tables.
-$$\csc ( 2 \pi )$$

Accepted Answer

A)  -1 
B)  1 
C)  0 
D)  Undefined 
A)  -1 
B)  1 
C)  0 
D)  Undefined

Question 8

Use the appropriate addition formula to find the exact value of the expression.
-$\sin \left( \frac { 19 \pi } { 12 } \right)$

Accepted Answer

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

Question 9

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.
-$y = - \cos ( \theta + \pi ) \quad$ Find C.

Accepted Answer

A)  $\frac { \pi } { 8 }$ 
B)  $- \frac { 1 } { 7 } \pi$ 
C)  $- \frac { 4 } { 7 } \pi$ 
D)  $- \frac { \pi } { 8 }$ 
A)  $\frac { \pi } { 8 }$ 
B)  $- \frac { 1 } { 7 } \pi$ 
C)  $- \frac { 4 } { 7 } \pi$ 
D)  $- \frac { \pi } { 8 }$

Question 10

Express as a single logarithm and, if possible, simplify.
-$\ln \cos \theta - \ln \left( \frac { \cos \theta } { 10 } \right)$

Accepted Answer

A)  $\ln \cos \theta$ 
B)  $\ln \left( \frac { 1 } { 10 } \right)$ 
C)  $\ln \left( \frac { \cos ^ { 2 } \theta } { 10 } \right)$ 
D)  $\ln 10$ 
A)  $\ln \cos \theta$ 
B)  $\ln \left( \frac { 1 } { 10 } \right)$ 
C)  $\ln \left( \frac { \cos ^ { 2 } \theta } { 10 } \right)$ 
D)  $\ln 10$

Question 11

The problem tells how many units and in what direction the graph of the given equation is to be shifted. Give an
equation for the shifted graph. Then sketch the original graph with a dashed line and the shifted graph with a solid line.
-$ y=x^{3} $
Down 6, left 5

Accepted Answer

A)  
A)  $y-6=(x-5)^{3}$
  
B)  $y+6=(x+5)^{3}$
  
C)  
C)  $y+6=(x-5)^{3}$
  
D)  $y-6=(x+5)^{3}$
  
A)  
A)  $y-6=(x-5)^{3}$
  
B)  $y+6=(x+5)^{3}$
  
C)  
C)  $y+6=(x-5)^{3}$
  
D)  $y-6=(x+5)^{3}$

Question 12

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)  $y = x ^ { 2 } + 3$ 
B)  $y = ( x - 3 ) ^ { 2 }$ 
C)  $y = x ^ { 2 } - 3$ 
D)  $y = ( x + 3 ) ^ { 2 }$ 
A)  $y = x ^ { 2 } + 3$ 
B)  $y = ( x - 3 ) ^ { 2 }$ 
C)  $y = x ^ { 2 } - 3$ 
D)  $y = ( x + 3 ) ^ { 2 }$

Question 13

Express the following logarithm as specified.
-$\ln ( 1 / 27 )$ in terms of $\ln 3$

Accepted Answer

A)  $3 \ln 27$ 
B)  $- 3 \ln 3$ 
C)  $\frac { 1 } { 3 } \ln 3$ 
D)  $- \frac { 1 } { 3 } \ln 3$ 
A)  $3 \ln 27$ 
B)  $- 3 \ln 3$ 
C)  $\frac { 1 } { 3 } \ln 3$ 
D)  $- \frac { 1 } { 3 } \ln 3$

Question 14

Graph the function.
-$$y = \frac { 1 } { x + 2 }$$

Accepted Answer

A) 
  
B) 
  
C)

D)

A) 
  
B) 
  
C)

D)

Question 15

Express the given quantity in terms of sin x or cos x.
-$\cos \left( \frac { 3 \pi } { 2 } - x \right)$

Accepted Answer

A)  $- \sin x$ 
B)  $\sin ( - x )$ 
C)  $\sin x$ 
D)  $\cos x + \sin x$ 
A)  $- \sin x$ 
B)  $\sin ( - x )$ 
C)  $\sin x$ 
D)  $\cos x + \sin x$

Question 16

Find the inverse of the function.
-$$f ( x ) = 2 x - 5$$

Accepted Answer

A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } - 5 } { 2 }$ 
B)  Not a one-to-one function 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } + 5 } { 2 }$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 2 } + 5$ 
A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } - 5 } { 2 }$ 
B)  Not a one-to-one function 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } + 5 } { 2 }$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 2 } + 5$

Question 17

Find the inverse of the function.
-$$f ( x ) = \sqrt { x } - 5 , x \geq 0$$

Accepted Answer

A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } + 5 , \mathrm { x } \geq 5$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = - ( \mathrm { x } + 5 ) ^ { 2 } , \mathrm { x } \geq 5$ 
C)  $f ^ { - 1 } ( x ) = ( x - 5 ) ^ { 2 }$ 
D)  $f ^ { - 1 } ( x ) = ( x + 5 ) ^ { 2 } , x \geq 5$ 
A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } + 5 , \mathrm { x } \geq 5$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = - ( \mathrm { x } + 5 ) ^ { 2 } , \mathrm { x } \geq 5$ 
C)  $f ^ { - 1 } ( x ) = ( x - 5 ) ^ { 2 }$ 
D)  $f ^ { - 1 } ( x ) = ( x + 5 ) ^ { 2 } , x \geq 5$

Question 18

Solve the problem.
-The purchasing power of a dollar is decreasing at the rate of 6.0% annually, compounded continuously. How long will it take for the purchasing power of $1.00 to be worth $0.81? Round answers to the nearest hundredth.

Accepted Answer

A)  13.50 yr 
B)  0.04 yr 
C)  0.35 yr 
D)  3.51 yr 
A)  13.50 yr 
B)  0.04 yr 
C)  0.35 yr 
D)  3.51 yr

Question 19

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 20

Simplify the expression.
-$$6 ^{log _ { 6 } 12}$$

Accepted Answer

A)  72 
B)  12 
C)  6 
D)  $\log _{6} 12$ 
A)  72 
B)  12 
C)  6 
D)  $\log _{6} 12$

Consider the function y Can x be 0? - $y = \sqrt { 1 - \frac { 1 } { x } }$

Find the domain and range of the function. - $\mathrm { F } ( \mathrm { t } ) = \mathrm { t } ^ { 2 } - 8$

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

Find the exact function value. - $\cos ^ { - 1 } \left( \frac { \sqrt { 2 } } { 2 } \right)$

Use a graphing calculator or computer to determine which of the given viewing windows displays the most appropriate graph of the specified function. - $f ( x ) = x ^ { 2 / 3 } ( 4 - x )$

Find the exact value of the trigonometric function. Do not use a calculator or tables. - $\csc ( 2 \pi )$

Use the appropriate addition formula to find the exact value of the expression. - $\sin \left( \frac { 19 \pi } { 12 } \right)$

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. - $y = - \cos ( \theta + \pi ) \quad$ Find C.

Express as a single logarithm and, if possible, simplify. - $\ln \cos \theta - \ln \left( \frac { \cos \theta } { 10 } \right)$

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

Express the following logarithm as specified. - $\ln ( 1 / 27 )$ in terms of $\ln 3$

Graph the function. - $y = \frac { 1 } { x + 2 }$ $Graph the function. - y = \frac { 1 } { x + 2 }$

Express the given quantity in terms of sin x or cos x. - $\cos \left( \frac { 3 \pi } { 2 } - x \right)$

Find the inverse of the function. - $f ( x ) = 2 x - 5$

Find the inverse of the function. - $f ( x ) = \sqrt { x } - 5 , x \geq 0$

Solve the problem. -The purchasing power of a dollar is decreasing at the rate of 6.0% annually, compounded continuously. How long will it take for the purchasing power of $1.00 to be worth $0.81? Round answers to the nearest hundredth.

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. - $6 ^{log _ { 6 } 12}$

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

Consider the function y Can x be 0? - y=1−1xy = \sqrt { 1 - \frac { 1 } { x } }y=1−x1​​

Find the domain and range of the function. - F(t)=t2−8\mathrm { F } ( \mathrm { t } ) = \mathrm { t } ^ { 2 } - 8F(t)=t2−8

Graph the function. - F(x)={4−x,x≤21−3x,x>2F ( x ) = \left\{ \begin{array} { l l } 4 - x , & x \leq 2 \\1 - 3 x , & x > 2\end{array} \right.F(x)={4−x,1−3x,​x≤2x>2​

The problem tells how many units and in what direction the graph of the given equation is to be shifted. Give an equation for the shifted graph. Then sketch the original graph with a dashed line and the shifted graph with a solid line. - y=−xy = - \sqrt { x }y=−x​ Left 6

Find the exact function value. - cos⁡−1(22)\cos ^ { - 1 } \left( \frac { \sqrt { 2 } } { 2 } \right)cos−1(22​​)

Use a graphing calculator or computer to determine which of the given viewing windows displays the most appropriate graph of the specified function. - f(x)=x2/3(4−x)f ( x ) = x ^ { 2 / 3 } ( 4 - x )f(x)=x2/3(4−x)

Find the exact value of the trigonometric function. Do not use a calculator or tables. - csc⁡(2π)\csc ( 2 \pi )csc(2π)

Use the appropriate addition formula to find the exact value of the expression. - sin⁡(19π12)\sin \left( \frac { 19 \pi } { 12 } \right)sin(1219π​)

For f(x)=Asin⁡(2πB(x−C))+Df ( x ) = A \sin \left( \frac { 2 \pi } { B } ( x - C ) \right) + Df(x)=Asin(B2π​(x−C))+D identify either A, B, C, or D as ind icated for the sine function. Find A. - y=−cos⁡(θ+π)y = - \cos ( \theta + \pi ) \quady=−cos(θ+π) Find C.

Express as a single logarithm and, if possible, simplify. - ln⁡cos⁡θ−ln⁡(cos⁡θ10)\ln \cos \theta - \ln \left( \frac { \cos \theta } { 10 } \right)lncosθ−ln(10cosθ​)

The problem tells how many units and in what direction the graph of the given equation is to be shifted. Give an equation for the shifted graph. Then sketch the original graph with a dashed line and the shifted graph with a solid line. - y=x3 y=x^{3} y=x3 Down 6, left 5

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.

Express the following logarithm as specified. - ln⁡(1/27)\ln ( 1 / 27 )ln(1/27) in terms of ln⁡3\ln 3ln3

Graph the function. - y=1x+2y = \frac { 1 } { x + 2 }y=x+21​

Express the given quantity in terms of sin x or cos x. - cos⁡(3π2−x)\cos \left( \frac { 3 \pi } { 2 } - x \right)cos(23π​−x)

Find the inverse of the function. - f(x)=2x−5f ( x ) = 2 x - 5f(x)=2x−5

Find the inverse of the function. - f(x)=x−5,x≥0f ( x ) = \sqrt { x } - 5 , x \geq 0f(x)=x​−5,x≥0