Question 1

Graph the function.
-$$y = \frac { 1 } { 5 x } + 1$$

Accepted Answer

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

Question 2

Find a formula for the function graphed.
-

Accepted Answer

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

Question 3

Consider the function y Can x be 0?
-Graph the equation |x| + |y| = 1 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 B

Question 4

One of sin x, cos x, and tan x is given. Find the other two if x lies in the specified interval.
-$$\cos x = \frac { 4 } { 5 } , \quad x \text { in } \left[ - \frac { \pi } { 2 } , 0 \right]$$

Accepted Answer

A)  $\sin x = - \frac { 3 } { 5 } , \tan x = - \frac { 3 } { 4 }$ 
B)  $\sin x = - \frac { 3 } { 5 } , \tan x = - \frac { 4 } { 3 }$ 
C)  $\sin x = \frac { 3 } { 5 } , \tan x = - \frac { 4 } { 3 }$ 
D)  $\sin x = \frac { 3 } { 5 } , \tan x = \frac { 3 } { 4 }$ 
A)  $\sin x = - \frac { 3 } { 5 } , \tan x = - \frac { 3 } { 4 }$ 
B)  $\sin x = - \frac { 3 } { 5 } , \tan x = - \frac { 4 } { 3 }$ 
C)  $\sin x = \frac { 3 } { 5 } , \tan x = - \frac { 4 } { 3 }$ 
D)  $\sin x = \frac { 3 } { 5 } , \tan x = \frac { 3 } { 4 }$

Question 5

Find the domain and graph the function.
-$F ( t ) = \frac { | t - 2 | } { t - 2 }$

Accepted Answer

A)  D: $( - \infty , 0 ) \cup ( 0 , \infty )$
  
B)  D: $( - \infty , 2 ) \cup ( 2 , \infty )$
  
C)  D: $( - \infty , 2 ) \cup ( 2 > , \infty )$
  
D)  D: $( - \infty , \infty )$
  
A)  D: $( - \infty , 0 ) \cup ( 0 , \infty )$
  
B)  D: $( - \infty , 2 ) \cup ( 2 , \infty )$
  
C)  D: $( - \infty , 2 ) \cup ( 2 > , \infty )$
  
D)  D: $( - \infty , \infty )$

Question 6

Solve for t or y, as appropriate.
-$$100 \mathrm { e } ^ { 8 \mathrm { t } } = 200$$

Accepted Answer

A)  $\frac { \mathrm { e } ^ { 2 } } { 8 }$ 
B)  $\frac { \ln 100 } { 8 }$ 
C)  $\frac { \ln 2 } { 8 }$ 
D)  $\ln \left( \frac { 1 } { 4 } \right)$ 
A)  $\frac { \mathrm { e } ^ { 2 } } { 8 }$ 
B)  $\frac { \ln 100 } { 8 }$ 
C)  $\frac { \ln 2 } { 8 }$ 
D)  $\ln \left( \frac { 1 } { 4 } \right)$

Question 7

Solve for t or y, as appropriate.
-$$\ln ( 9 - 4 y ) = x$$

Accepted Answer

A)  $\frac { 9 - \mathrm { e } ^ { \mathrm { X } } } { 4 }$ 
B)  $\frac { 9 - \ln x } { 4 }$ 
C)  $e ^ { x } - 5$ 
D)  $\frac { e ^ { x } - 9 } { 4 }$ 
A)  $\frac { 9 - \mathrm { e } ^ { \mathrm { X } } } { 4 }$ 
B)  $\frac { 9 - \ln x } { 4 }$ 
C)  $e ^ { x } - 5$ 
D)  $\frac { e ^ { x } - 9 } { 4 }$

Question 8

The problem tells by what factor and direction the graph of the given function is to be stretched or compressed. Give an
equation for the stretched or compressed graph.
-$y = x ^ { 3 } + 1 \quad$ stretched vertically by a factor of 5

Accepted Answer

A)  $y = 125 x ^ { 3 } + 1$ 
B)  $y = \frac { x ^ { 3 } } { 5 } + \frac { 1 } { 5 }$ 
C)  $y = 5 x ^ { 3 } + 1$ 
D)  $y = 5 x ^ { 3 } + 5$ 
A)  $y = 125 x ^ { 3 } + 1$ 
B)  $y = \frac { x ^ { 3 } } { 5 } + \frac { 1 } { 5 }$ 
C)  $y = 5 x ^ { 3 } + 1$ 
D)  $y = 5 x ^ { 3 } + 5$

Question 9

Express as a single logarithm and, if possible, simplify.
-$\ln ( 6 \sec \theta ) + \ln ( 2 \cos \theta )$

Accepted Answer

A)  $\ln ( 12 \cot \theta )$ 
B)  $\ln ( 3 )$ 
C)  $\ln ( 6 \sec \theta + 2 \cos \theta )$ 
D)  $\ln ( 12 )$ 
A)  $\ln ( 12 \cot \theta )$ 
B)  $\ln ( 3 )$ 
C)  $\ln ( 6 \sec \theta + 2 \cos \theta )$ 
D)  $\ln ( 12 )$

Question 10

Solve the problem.
-An economist predicts that the buying power $B ( x )$ of a dollar $x$ years from now will decrease according to the formula $\mathrm { B } ( \mathrm { x } ) = 0.78 ^ { \mathrm { x } }$. How much will today's dollar be worth in 4 years? Round the answer to the nearest cent.

Accepted Answer

A)  $2.95 
B)  $3.12 
C)  $0.37 
D)  $0.91 
A)  $2.95 
B)  $3.12 
C)  $0.37 
D)  $0.91

Question 11

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

Accepted Answer

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

D)  Increasing $- \infty < x < 0$
Decreasing $0 < x < \infty$

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

D)  Increasing $- \infty < x < 0$
Decreasing $0 < x < \infty$

Question 12

Rewrite the ratio as a ratio of natural logarithms and simplify.
-$\frac { \log _ { \sqrt { 5 } } x } { \log _ { \sqrt { 3 } } x }$

Accepted Answer

A)  $\frac { 5 } { 3 }$ 
B)  $\sqrt { \frac { 5 } { 3 } }$ 
C)  $\sqrt { \frac { \ln 5 } { \ln 3 } }$ 
D)  $\frac { \ln 3 } { \ln 5 }$ 
A)  $\frac { 5 } { 3 }$ 
B)  $\sqrt { \frac { 5 } { 3 } }$ 
C)  $\sqrt { \frac { \ln 5 } { \ln 3 } }$ 
D)  $\frac { \ln 3 } { \ln 5 }$

Question 13

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

Accepted Answer

A)  Domain and range: all real numbers 
B)  Domain: $[ 0 , \infty )$; range: $[ 4 , \infty )$ 
C)  Domain: $[ 4 , \infty )$; range: $[ 4 , \infty )$ 
D)  Domain: $[ 4 , \infty )$; range: $[ 0 , \infty )$ 
A)  Domain and range: all real numbers 
B)  Domain: $[ 0 , \infty )$; range: $[ 4 , \infty )$ 
C)  Domain: $[ 4 , \infty )$; range: $[ 4 , \infty )$ 
D)  Domain: $[ 4 , \infty )$; range: $[ 0 , \infty )$

Question 14

Find a formula for the function graphed.
-

Accepted Answer

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

Question 15

Graph the function.
-$\text { Graph the function } f ( x ) = \sin 4 x + \cos 2 x \text {. }$

Accepted Answer

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

Question 16

Solve the problem.
-The population of a small country increases according to the functio $$\mathrm { B } = 1,800,000 \mathrm { e } ^ { 0.05 \mathrm { t } }$$ , where t is measured in years. How many people will the country have after 6 years?

Accepted Answer

A)  941,182 people 
B)  2,167,151 people 
C)  3,591,472 people 
D)  2,429,746 people 
A)  941,182 people 
B)  2,167,151 people 
C)  3,591,472 people 
D)  2,429,746 people

Question 17

Graph the function in the ts-plane (t-axis horizontal, s-axis vertical). State the period and symmetry of the function.
-$$s = \csc \left( \frac { \pi t } { 2 } \right)$$

Accepted Answer

A)  Period 4, symmetric about the s-axis
  
B)  Period 4, symmetric about the origin
  
C)  Period 4, symmetric about the origin
  
D)  Period 4, symmetric about the s-axis
  
A)  Period 4, symmetric about the s-axis
  
B)  Period 4, symmetric about the origin
  
C)  Period 4, symmetric about the origin
  
D)  Period 4, symmetric about the s-axis

Question 18

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

Question 19

Find the domain and range for the indicated function.
-$f ( x ) = \sqrt { x + 11 }$ $g ( x ) = \sqrt { x - 11 }$;
$g - f$

Accepted Answer

A)  D: $x \geq 11$
R: $\mathrm { y } \geq \sqrt { 22 }$ 
B)  D: $x \geq 11$
R: $y \geq - \sqrt { 22 }$ 
C)  D: $x \geq 11$
R: $\mathrm { y } \geq 0$ 
D)  D: $x \geq - 11$
R: $\mathrm { y } \geq - \sqrt { 22 }$ 
A)  D: $x \geq 11$
R: $\mathrm { y } \geq \sqrt { 22 }$ 
B)  D: $x \geq 11$
R: $y \geq - \sqrt { 22 }$ 
C)  D: $x \geq 11$
R: $\mathrm { y } \geq 0$ 
D)  D: $x \geq - 11$
R: $\mathrm { y } \geq - \sqrt { 22 }$

Question 20

The problem tells by what factor and direction the graph of the given function is to be stretched or compressed. Give an
equation for the stretched or compressed graph.
-$y = \sqrt { x + 1 } \quad$ compressed vertically by a factor of 7

Accepted Answer

A)  $y = \frac { \sqrt { x + 1 } } { 7 }$ 
B)  $y = 7 \sqrt { x + 1 }$ 
C)  $y = \sqrt { 7 x + 7 }$ 
D)  $y = \sqrt { 7 x + 1 }$ 
A)  $y = \frac { \sqrt { x + 1 } } { 7 }$ 
B)  $y = 7 \sqrt { x + 1 }$ 
C)  $y = \sqrt { 7 x + 7 }$ 
D)  $y = \sqrt { 7 x + 1 }$

Graph the function. - $y = \frac { 1 } { 5 x } + 1$ $Graph the function. - y = \frac { 1 } { 5 x } + 1$

Find a formula for the function graphed. -

Consider the function y Can x be 0? -Graph the equation |x| + |y| = 1 and decide whether or not the graph represents a function of x.

One of sin x, cos x, and tan x is given. Find the other two if x lies in the specified interval. - $\cos x = \frac { 4 } { 5 } , \quad x \text { in } \left[ - \frac { \pi } { 2 } , 0 \right]$

Find the domain and graph the function. - $F ( t ) = \frac { | t - 2 | } { t - 2 }$ $Find the domain and graph the function. - F ( t ) = \frac { | t - 2 | } { t - 2 }$

Solve for t or y, as appropriate. - $100 \mathrm { e } ^ { 8 \mathrm { t } } = 200$

Solve for t or y, as appropriate. - $\ln ( 9 - 4 y ) = x$

The problem tells by what factor and direction the graph of the given function is to be stretched or compressed. Give an equation for the stretched or compressed graph. - $y = x ^ { 3 } + 1 \quad$ stretched vertically by a factor of 5

Express as a single logarithm and, if possible, simplify. - $\ln ( 6 \sec \theta ) + \ln ( 2 \cos \theta )$

Solve the problem. -An economist predicts that the buying power $B ( x )$ of a dollar $x$ years from now will decrease according to the formula $\mathrm { B } ( \mathrm { x } ) = 0.78 ^ { \mathrm { x } }$ . How much will today's dollar be worth in 4 years? Round the answer to the nearest cent.

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

Rewrite the ratio as a ratio of natural logarithms and simplify. - $\frac { \log _ { \sqrt { 5 } } x } { \log _ { \sqrt { 3 } } x }$

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

Find a formula for the function graphed. -

Graph the function. - $\text { Graph the function } f ( x ) = \sin 4 x + \cos 2 x \text {. }$ $Graph the function. - \text { Graph the function } f ( x ) = \sin 4 x + \cos 2 x \text {. }$

Solve the problem. -The population of a small country increases according to the functio $\mathrm { B } = 1,800,000 \mathrm { e } ^ { 0.05 \mathrm { t } }$ , where t is measured in years. How many people will the country have after 6 years?

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

Find the domain and range for the indicated function. - $f ( x ) = \sqrt { x + 11 }$ $g ( x ) = \sqrt { x - 11 }$ ; $g - f$

The problem tells by what factor and direction the graph of the given function is to be stretched or compressed. Give an equation for the stretched or compressed graph. - $y = \sqrt { x + 1 } \quad$ compressed vertically by a factor of 7

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

Graph the function. - y=15x+1y = \frac { 1 } { 5 x } + 1y=5x1​+1

Find a formula for the function graphed. -

Consider the function y Can x be 0? -Graph the equation |x| + |y| = 1 and decide whether or not the graph represents a function of x.

One of sin x, cos x, and tan x is given. Find the other two if x lies in the specified interval. - cos⁡x=45,x in [−π2,0]\cos x = \frac { 4 } { 5 } , \quad x \text { in } \left[ - \frac { \pi } { 2 } , 0 \right]cosx=54​,x in [−2π​,0]

Find the domain and graph the function. - F(t)=∣t−2∣t−2F ( t ) = \frac { | t - 2 | } { t - 2 }F(t)=t−2∣t−2∣​

Solve for t or y, as appropriate. - 100e8t=200100 \mathrm { e } ^ { 8 \mathrm { t } } = 200100e8t=200

Solve for t or y, as appropriate. - ln⁡(9−4y)=x\ln ( 9 - 4 y ) = xln(9−4y)=x

The problem tells by what factor and direction the graph of the given function is to be stretched or compressed. Give an equation for the stretched or compressed graph. - y=x3+1y = x ^ { 3 } + 1 \quady=x3+1 stretched vertically by a factor of 5

Express as a single logarithm and, if possible, simplify. - ln⁡(6sec⁡θ)+ln⁡(2cos⁡θ)\ln ( 6 \sec \theta ) + \ln ( 2 \cos \theta )ln(6secθ)+ln(2cosθ)

Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - y=1xy=\frac{1}{x}y=x1​

Rewrite the ratio as a ratio of natural logarithms and simplify. - log⁡5xlog⁡3x\frac { \log _ { \sqrt { 5 } } x } { \log _ { \sqrt { 3 } } x }log3​​xlog5​​x​

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

Find a formula for the function graphed. -

Graph the function. - Graph the function f(x)=sin⁡4x+cos⁡2x. \text { Graph the function } f ( x ) = \sin 4 x + \cos 2 x \text {. } Graph the function f(x)=sin4x+cos2x.

Solve the problem. -The population of a small country increases according to the functio B=1,800,000e0.05t\mathrm { B } = 1,800,000 \mathrm { e } ^ { 0.05 \mathrm { t } }B=1,800,000e0.05t , where t is measured in years. How many people will the country have after 6 years?

Graph the function in the ts-plane (t-axis horizontal, s-axis vertical). State the period and symmetry of the function. - s=csc⁡(πt2)s = \csc \left( \frac { \pi t } { 2 } \right)s=csc(2πt​)

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 domain and range for the indicated function. - f(x)=x+11f ( x ) = \sqrt { x + 11 }f(x)=x+11​ g(x)=x−11g ( x ) = \sqrt { x - 11 }g(x)=x−11​ ; g−fg - fg−f

The problem tells by what factor and direction the graph of the given function is to be stretched or compressed. Give an equation for the stretched or compressed graph. - y=x+1y = \sqrt { x + 1 } \quady=x+1​ compressed vertically by a factor of 7

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

Graph the function. - $y = \frac { 1 } { 5 x } + 1$ $Graph the function. - y = \frac { 1 } { 5 x } + 1$

One of sin x, cos x, and tan x is given. Find the other two if x lies in the specified interval. - $\cos x = \frac { 4 } { 5 } , \quad x \text { in } \left[ - \frac { \pi } { 2 } , 0 \right]$

Find the domain and graph the function. - $F ( t ) = \frac { | t - 2 | } { t - 2 }$ $Find the domain and graph the function. - F ( t ) = \frac { | t - 2 | } { t - 2 }$

Solve for t or y, as appropriate. - $100 \mathrm { e } ^ { 8 \mathrm { t } } = 200$

Solve for t or y, as appropriate. - $\ln ( 9 - 4 y ) = x$

The problem tells by what factor and direction the graph of the given function is to be stretched or compressed. Give an equation for the stretched or compressed graph. - $y = x ^ { 3 } + 1 \quad$ stretched vertically by a factor of 5

Express as a single logarithm and, if possible, simplify. - $\ln ( 6 \sec \theta ) + \ln ( 2 \cos \theta )$

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

Rewrite the ratio as a ratio of natural logarithms and simplify. - $\frac { \log _ { \sqrt { 5 } } x } { \log _ { \sqrt { 3 } } x }$

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

Graph the function. - $\text { Graph the function } f ( x ) = \sin 4 x + \cos 2 x \text {. }$ $Graph the function. - \text { Graph the function } f ( x ) = \sin 4 x + \cos 2 x \text {. }$

Solve the problem. -The population of a small country increases according to the functio $\mathrm { B } = 1,800,000 \mathrm { e } ^ { 0.05 \mathrm { t } }$ , where t is measured in years. How many people will the country have after 6 years?

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

Find the domain and range for the indicated function. - $f ( x ) = \sqrt { x + 11 }$ $g ( x ) = \sqrt { x - 11 }$ ; $g - f$

The problem tells by what factor and direction the graph of the given function is to be stretched or compressed. Give an equation for the stretched or compressed graph. - $y = \sqrt { x + 1 } \quad$ compressed vertically by a factor of 7