Question 1

Identify which of the twelve basic functions listed below fit the description given.
-The three functions that are even

Accepted Answer

A)  $y = x ^ { 2 } , y = \cos x , y = | x |$ 
B)  $y = x , y = x ^ { 2 } , y = x ^ { 3 }$ 
C)  $y = x , y = \frac { 1 } { x } , y = x ^ { 3 }$ 
D)  $y = \cos x , y = \sin x , y = | x |$ 
A)  $y = x ^ { 2 } , y = \cos x , y = | x |$ 
B)  $y = x , y = x ^ { 2 } , y = x ^ { 3 }$ 
C)  $y = x , y = \frac { 1 } { x } , y = x ^ { 3 }$ 
D)  $y = \cos x , y = \sin x , y = | x |$

Question 2

Solve the problem.
-Use the graph of $f$ to estimate the local maximum and local minimum.

Accepted Answer

A)  Local maximum: 0 and 1 ; local minimum: 0 and $- 1$ 
B)  Local maximum: 1; local minimum: $- 1$ 
C)  Local maximum: 1; local minimum: 0 and $- 1$ 
D)  Local maximum: 0 and 1 ; local minimum: $- 1$ 
A)  Local maximum: 0 and 1 ; local minimum: 0 and $- 1$ 
B)  Local maximum: 1; local minimum: $- 1$ 
C)  Local maximum: 1; local minimum: 0 and $- 1$ 
D)  Local maximum: 0 and 1 ; local minimum: $- 1$

Question 3

Determine whether the formula determines y as a function of x.
-$$x = y ^ { 2 } - 9$$

Accepted Answer

A) True 
 B)False

Question 4

Give the equation of the function g whose graph is described.
-The graph of $\mathrm { f } ( \mathrm { x } ) = \mathrm { x } ^ { 2 }$ is vertically stretched by a factor of 8 , and the resulting graph is reflected across the $x$-axis.

Accepted Answer

A)  $g ( x ) = - 8 x ^ { 2 }$ 
B)  $g ( x ) = ( x - 8 ) ^ { 2 }$ 
C)  $g ( x ) = 8 ( x - 8 ) x ^ { 2 }$ 
D)  $g ( x ) = 8 x ^ { 2 }$ 
A)  $g ( x ) = - 8 x ^ { 2 }$ 
B)  $g ( x ) = ( x - 8 ) ^ { 2 }$ 
C)  $g ( x ) = 8 ( x - 8 ) x ^ { 2 }$ 
D)  $g ( x ) = 8 x ^ { 2 }$

Question 5

Write the word or phrase that best completes each statement or answers the question.
Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.
-$$f ( x ) = \frac { x + 7 } { x } \text { and } g ( x ) = \frac { 7 } { x - 1 }$$

Accepted Answer

\[\begin{array} { l } 
f ( g ( x ) ) = \

Question 6

Sketch the graph of y1 as a solid line or curve. Then sketch the graph of y2 as a dashed line or curve by one or more of
these: a vertical and/or horizontal shift of the graph y1, a vertical stretch or shrink of the graph of y1, or a reflection of the
graph of y1 across an axis.
-$y_{1}=x^{2} ; y_{2}=(x-3)^{2}-5$

Accepted Answer

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

Question 7

Write the word or phrase that best completes each statement or answers the question.
Graph the function on your calculator in order to answer the following questions:
On what intervals is the function increasing? decreasing?
Is the function odd, even, or neither?
Give the function's extrema, if any.
Find the horizontal asymptotes, if any.
How does the graph relate to a graph of one of the twelve basic functions?
-$$f ( x ) = e ^ { - x }$$

Accepted Answer

Decreasing on @#LAT-DLM&
Neither odd nor

Question 8

Sketch the graph of y1 as a solid line or curve. Then sketch the graph of y2 as a dashed line or curve by one or more of
these: a vertical and/or horizontal shift of the graph y1, a vertical stretch or shrink of the graph of y1, or a reflection of the
graph of y1 across an axis.
-$$y _ { 1 } = | x | y _ { 2 } = \frac { 1 } { 4 } | x + 5 | - 6$$

Accepted Answer

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

Question 9

Graph the function on your calculator to determine the domain and range from the graph.
-$$g ( x ) = \frac { 1 } { 1 + e ^ { - x } } - 3$$

Accepted Answer

A)  Domain: $( - \infty , \infty )$; range: $( - 3 , - 2 )$ 
B)  Domain: $( - \infty , \infty )$; range: $( - \infty , - 2 ]$ 
C)  Domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$ 
D)  Domain: $( 0 , \infty )$; range: $[ - 3 , - 2 ]$ 
A)  Domain: $( - \infty , \infty )$; range: $( - 3 , - 2 )$ 
B)  Domain: $( - \infty , \infty )$; range: $( - \infty , - 2 ]$ 
C)  Domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$ 
D)  Domain: $( 0 , \infty )$; range: $[ - 3 , - 2 ]$

Question 10

Determine whether the graph is the graph of a function.
-

Accepted Answer

A) True 
 B)False

Question 11

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-$$y = x ^ { 2 } + 3$$

Accepted Answer

A)  Shift the graph of $y = x ^ { 2 }$ right 3 units. 
B)  Shift the graph of $y = x ^ { 2 }$ up 3 units. 
C)  Shift the graph of $y = x ^ { 2 }$ down 3 units. 
D)  Shift the graph of $y = x ^ { 2 }$ left 3 units. 
A)  Shift the graph of $y = x ^ { 2 }$ right 3 units. 
B)  Shift the graph of $y = x ^ { 2 }$ up 3 units. 
C)  Shift the graph of $y = x ^ { 2 }$ down 3 units. 
D)  Shift the graph of $y = x ^ { 2 }$ left 3 units.

Question 12

Solve the problem.
-A traveling salesperson averaged 48 miles per hour on a 246 mile trip. How many hours were spent on the trip?

Accepted Answer

A)  2.56 hours 
B)  0.2 hours 
C)  198 hours 
D)  5.13 hours 
A)  2.56 hours 
B)  0.2 hours 
C)  198 hours 
D)  5.13 hours

Question 13

Graph the function on your calculator to determine the domain and range from the graph.
-$$h ( x ) = | x - 6 |$$

Accepted Answer

A)  Domain: $[ 0 , \infty )$; range: $( - \infty , \infty )$ 
B)  Domain: $( - \infty , \infty )$; range: $[ 6 , \infty )$ 
C)  Domain: $[ 6 , \infty )$; range: $[ 0 , \infty )$ 
D)  Domain: $( - \infty , \infty )$; range: $[ 0 , \infty )$ 
A)  Domain: $[ 0 , \infty )$; range: $( - \infty , \infty )$ 
B)  Domain: $( - \infty , \infty )$; range: $[ 6 , \infty )$ 
C)  Domain: $[ 6 , \infty )$; range: $[ 0 , \infty )$ 
D)  Domain: $( - \infty , \infty )$; range: $[ 0 , \infty )$

Question 14

Find the range of the function.
-$$f ( x ) = \frac { 16 } { 15 - x }$$

Accepted Answer

A)  $( - \infty , 15 ) \cup ( 15 , \infty )$ 
B)  $( - \infty , 0 ) \cup ( 0 , \infty )$ 
C)  $( - \infty , \infty )$ 
D)  $( 0 , \infty )$ 
A)  $( - \infty , 15 ) \cup ( 15 , \infty )$ 
B)  $( - \infty , 0 ) \cup ( 0 , \infty )$ 
C)  $( - \infty , \infty )$ 
D)  $( 0 , \infty )$

Question 15

Solve the problem.
-Estimate graphically the local maximum and local minimum of $f ( x ) = 0.0001 x ^ { 4 } - 0.1 x ^ { 2 } + 0.1$.

Accepted Answer

A)  Local maximum: $0.1$; local minima: $\pm 24.9$ 
B)  Local maximum: 0 ; no local minimum 
C)  Local maximum: 0.1; no local minimum 
D)  Local maximum: 0; local minima: $\pm 22.4$ 
A)  Local maximum: $0.1$; local minima: $\pm 24.9$ 
B)  Local maximum: 0 ; no local minimum 
C)  Local maximum: 0.1; no local minimum 
D)  Local maximum: 0; local minima: $\pm 22.4$

Question 16

Give the equation of the function g whose graph is described.
-The graph of $f ( x ) = \left| x ^ { 2 } + 6 x \right|$ is horizontally stretched by a factor of 3 .

Accepted Answer

A)  $g ( x ) = 3 \left| x ^ { 2 } + 6 x \right|$ 
B)  $g ( x ) = \left| \frac { 1 } { 3 } x ^ { 2 } + 2 x \right|$ 
C)  $g ( x ) = \left| 9 x ^ { 2 } + 18 x \right|$ 
D)  $g ( x ) = \left| \frac { 1 } { 9 } x ^ { 2 } + 2 x \right|$ 
A)  $g ( x ) = 3 \left| x ^ { 2 } + 6 x \right|$ 
B)  $g ( x ) = \left| \frac { 1 } { 3 } x ^ { 2 } + 2 x \right|$ 
C)  $g ( x ) = \left| 9 x ^ { 2 } + 18 x \right|$ 
D)  $g ( x ) = \left| \frac { 1 } { 9 } x ^ { 2 } + 2 x \right|$

Question 17

Find the inverse of the function.
-$$f ( x ) = \sqrt [ 3 ] { \frac { x } { 9 } } - 8$$

Accepted Answer

A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = 27 ( \mathrm { x } + 8 )$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = 9 ( \mathrm { x } + 8 ) ^ { 3 }$ 
C)  $f ^ { - 1 } ( x ) = 9 \left( x ^ { 3 } + 8 \right)$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = [ 9 ( \mathrm { x } + 8 ) ] ^ { 3 }$ 
A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = 27 ( \mathrm { x } + 8 )$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = 9 ( \mathrm { x } + 8 ) ^ { 3 }$ 
C)  $f ^ { - 1 } ( x ) = 9 \left( x ^ { 3 } + 8 \right)$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = [ 9 ( \mathrm { x } + 8 ) ] ^ { 3 }$

Question 18

Match the function with the graph.
-

Accepted Answer

A)  $y = \sin x + 1$ 
B)  $y = \cos x - 1$ 
C)  $y = \cos ( x + 1 )$ 
D)  $y = \sin x - 1$ 
A)  $y = \sin x + 1$ 
B)  $y = \cos x - 1$ 
C)  $y = \cos ( x + 1 )$ 
D)  $y = \sin x - 1$

Question 19

Choose the one alternative that best completes the statement or answers the question.
Write a mathematical expression for the quantity described verbally.
-The profit consists of a franchise fee of $\$ 100,000$ plus $20 \%$ of all sales

Accepted Answer

A)  $0.2 + 100,000 x$ 
B)  $20 x + 100,000$ 
C)  $( 0.2 x + 100,000 )$ 
D)  $\$ 100,000 - 0.2$ 
A)  $0.2 + 100,000 x$ 
B)  $20 x + 100,000$ 
C)  $( 0.2 x + 100,000 )$ 
D)  $\$ 100,000 - 0.2$

Question 20

Solve the problem.
-Some of the results of an analysis, on the makeup of garbage, are given in the following table. The table displays various years which gives the number of pounds per person per day of various types of waste materials.

For plastics, calculate the average rates of change between consecutive data points in the table. Interpret the mea your results.

Accepted Answer

A)  The rate of increase decreases from each decade to the next. 
B)  The rate of increase increases from each decade to the next. 
C)  The rate of increase decreases during the 1990 's, but then increases during 2000-2008. 
D)  The rate of increase increases during the 1990 's, but then decreases during the 2000-2008. 
A)  The rate of increase decreases from each decade to the next. 
B)  The rate of increase increases from each decade to the next. 
C)  The rate of increase decreases during the 1990 's, but then increases during 2000-2008. 
D)  The rate of increase increases during the 1990 's, but then decreases during the 2000-2008.

Identify which of the twelve basic functions listed below fit the description given. -The three functions that are even

Solve the problem. -Use the graph of $f$ to estimate the local maximum and local minimum.

Determine whether the formula determines y as a function of x. - $x = y ^ { 2 } - 9$

Give the equation of the function g whose graph is described. -The graph of $\mathrm { f } ( \mathrm { x } ) = \mathrm { x } ^ { 2 }$ is vertically stretched by a factor of 8 , and the resulting graph is reflected across the $x$ -axis.

Write the word or phrase that best completes each statement or answers the question. Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. - $f ( x ) = \frac { x + 7 } { x } \text { and } g ( x ) = \frac { 7 } { x - 1 }$

Graph the function on your calculator to determine the domain and range from the graph. - $g ( x ) = \frac { 1 } { 1 + e ^ { - x } } - 3$

Determine whether the graph is the graph of a function. -

Choose the one alternative that best completes the statement or answers the question. Solve the problem. - $y = x ^ { 2 } + 3$

Solve the problem. -A traveling salesperson averaged 48 miles per hour on a 246 mile trip. How many hours were spent on the trip?

Graph the function on your calculator to determine the domain and range from the graph. - $h ( x ) = | x - 6 |$

Find the range of the function. - $f ( x ) = \frac { 16 } { 15 - x }$

Solve the problem. -Estimate graphically the local maximum and local minimum of $f ( x ) = 0.0001 x ^ { 4 } - 0.1 x ^ { 2 } + 0.1$ .

Give the equation of the function g whose graph is described. -The graph of $f ( x ) = \left| x ^ { 2 } + 6 x \right|$ is horizontally stretched by a factor of 3 .

Find the inverse of the function. - $f ( x ) = \sqrt [ 3 ] { \frac { x } { 9 } } - 8$

Match the function with the graph. -

Choose the one alternative that best completes the statement or answers the question. Write a mathematical expression for the quantity described verbally. -The profit consists of a franchise fee of $\$ 100,000$ plus $20 \%$ of all sales

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Exam 1: Functions and Graphs