Question 1

Identify intervals on which the function is increasing, decreasing, or constant.
-$$g ( x ) = 2 - ( x - 5 ) ^ { 2 }$$

Accepted Answer

A)  Increasing: $( - \infty , 5 )$; decreasing: $( 5 , \infty )$ 
B)  Increasing: $( - \infty , - 5 )$; decreasing: $( - 5 , \infty )$ 
C)  Increasing: $( 2 , \infty )$; decreasing: $( - \infty , 2 )$ 
D)  Increasing: $( - \infty , 2 )$; decreasing: $( 2 , \infty )$ 
A)  Increasing: $( - \infty , 5 )$; decreasing: $( 5 , \infty )$ 
B)  Increasing: $( - \infty , - 5 )$; decreasing: $( - 5 , \infty )$ 
C)  Increasing: $( 2 , \infty )$; decreasing: $( - \infty , 2 )$ 
D)  Increasing: $( - \infty , 2 )$; decreasing: $( 2 , \infty )$

Question 2

Solve the problem.
-A ball is shot up in the air and its height, $h$, above the ground in feet is given by the function $h ( x ) = - 16 x ^ { 2 } + 46 x$, where $x$ is the number of seconds the ball has been in flight. Graph this function and find the maximum height that the ball attains. Round your answer to the hundredths place.

Accepted Answer

A)  $30.49$ 
B)  $33.06$ 
C)  $34.00$ 
D)  $34.40$ 
A)  $30.49$ 
B)  $33.06$ 
C)  $34.00$ 
D)  $34.40$

Question 3

Write the word or phrase that best completes each statement or answers the question.
Sketch the graph of the given function based on the graph of the function f given below.
-$$\text { Sketch the graph of } y = f ( 3 x ) \text {. }$$

Accepted Answer

The answer of Write the word or phrase that best...

Question 4

Tell which of the following types of regression is likely to give the most accurate model for the scatter plot shown: linear
regression, quadratic regression, cubic regression, exponential regression, sinusoidal regression.
-

Accepted Answer

A)  Quadratic regression 
B)  Cubic regression 
C)  Sinusoidal regression 
D)  Linear regression 
E)  Exponential regression 
A)  Quadratic regression 
B)  Cubic regression 
C)  Sinusoidal regression 
D)  Linear regression 
E)  Exponential regression

Question 5

Solve the problem.
-Helen Weller invested $14,000 in an account that pays 10% simple interest. How much additional money must be invested in an account that pays 13% simple interest so that the average return on the two investments
Amounts to 11%?

Accepted Answer

A)  $10,000 
B)  $7000 
C)  $11,000 
D)  $14,000 
A)  $10,000 
B)  $7000 
C)  $11,000 
D)  $14,000

Question 6

Solve the problem.
-A ball is shot up in the air and its height, $h$, above the ground in feet is given by the function $h ( x ) = - 16 x ^ { 2 } + 45 x$, where $x$ is the number of seconds the ball has been in flight. Graph this function and find the $x$-value for which the maximum height of the ball is attained. Round your answer to the hundredths place.

Accepted Answer

A)  $1.41$ 
B)  $1.30$ 
C)  $1.68$ 
D)  $1.53$ 
A)  $1.41$ 
B)  $1.30$ 
C)  $1.68$ 
D)  $1.53$

Question 7

Identify intervals on which the function is increasing, decreasing, or constant.
-$$f ( x ) = | x - 7 | - 3$$

Accepted Answer

A)  Increasing: $( - 7 , \infty )$; decreasing: $( - \infty , - 7 )$ 
B)  Increasing: $( - 3 , \infty )$; decreasing: $( - \infty , - 3 )$ 
C)  Increasing: $( 7 , \infty )$; decreasing: $( - \infty , 7 )$ 
D)  increasing: $( - \infty , 7 )$; decreasing: $( 7 , \infty )$ 
A)  Increasing: $( - 7 , \infty )$; decreasing: $( - \infty , - 7 )$ 
B)  Increasing: $( - 3 , \infty )$; decreasing: $( - \infty , - 3 )$ 
C)  Increasing: $( 7 , \infty )$; decreasing: $( - \infty , 7 )$ 
D)  increasing: $( - \infty , 7 )$; decreasing: $( 7 , \infty )$

Question 8

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-$$y = ( x - 18 ) ^ { 2 }$$

Accepted Answer

A)  Shift the graph of $y = x ^ { 2 }$ down 18 units. 
B)  Shift the graph of $y = x ^ { 2 }$ left 18 units. 
C)  Shift the graph of $y = x ^ { 2 }$ right 18 units. 
D)  Shift the graph of $y = x ^ { 2 }$ up 18 units. 
A)  Shift the graph of $y = x ^ { 2 }$ down 18 units. 
B)  Shift the graph of $y = x ^ { 2 }$ left 18 units. 
C)  Shift the graph of $y = x ^ { 2 }$ right 18 units. 
D)  Shift the graph of $y = x ^ { 2 }$ up 18 units.

Question 9

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 10

Graph the function on your calculator to determine the domain and range from the graph.
-$$f ( x ) = \frac { 1 } { x } + 2$$

Accepted Answer

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

Question 11

Give the equation of the function g whose graph is described.
-The graph of $\mathrm { f } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } }$ is shifted $4.2$ units to the left. This graph is then vertically stretched by a factor of $3.3 .$ Finally, the graph is reflected across the $x$-axis.

Accepted Answer

A)  $g ( x ) = - 3.3 \sqrt [ 3 ] { x + 4.2 }$ 
B)  $g ( x ) = - 4.2 \sqrt [ 3 ] { x + 3.3 }$ 
C)  $g ( x ) = 3.3 \sqrt [ 3 ] { x + 4.2 }$ 
D)  $g ( x ) = - 3.3 \sqrt [ 3 ] { x - 4.2 }$ 
A)  $g ( x ) = - 3.3 \sqrt [ 3 ] { x + 4.2 }$ 
B)  $g ( x ) = - 4.2 \sqrt [ 3 ] { x + 3.3 }$ 
C)  $g ( x ) = 3.3 \sqrt [ 3 ] { x + 4.2 }$ 
D)  $g ( x ) = - 3.3 \sqrt [ 3 ] { x - 4.2 }$

Question 12

Perform the requested operation or operations.
-$f ( x ) = \frac { x - 9 } { 5 } ; g ( x ) = 5 x + 9$, find $g ( f ( x ) )$

Accepted Answer

A)  $g ( f ( x ) ) = 5 x + 36$ 
B)  $g ( f ( x ) ) = x$ 
C)  $g ( f ( x ) ) = x - \frac { 9 } { 5 }$ 
D)  $g ( f ( x ) ) = x + 18$ 
A)  $g ( f ( x ) ) = 5 x + 36$ 
B)  $g ( f ( x ) ) = x$ 
C)  $g ( f ( x ) ) = x - \frac { 9 } { 5 }$ 
D)  $g ( f ( x ) ) = x + 18$

Question 13

Determine if the function is bounded above, bounded below, bounded on its domain, or unbounded on its domain.
-$$y = 4 ^ { - x } + 6$$

Accepted Answer

A)  Bounded above 
B)  Bounded below 
C)  Bounded 
D)  Unbounded 
A)  Bounded above 
B)  Bounded below 
C)  Bounded 
D)  Unbounded

Question 14

Determine if the function is bounded above, bounded below, bounded on its domain, or unbounded on its domain.
-$$y = 30$$

Accepted Answer

A)  Unbounded 
B)  Bounded below 
C)  Bounded above 
D)  Bounded 
A)  Unbounded 
B)  Bounded below 
C)  Bounded above 
D)  Bounded

Question 15

Describe how to transform the graph of f into the graph of g.
-$$f ( x ) = \sqrt { x - 3 } \text { and } g ( x ) = \sqrt { x + 6 }$$

Accepted Answer

A)  Shift the graph of $f$ left 9 units. 
B)  Shift the graph of f right 3 units. 
C)  Shift the graph of $f$ left 3 units. 
D)  Shift the graph of $f$ right 9 units. 
A)  Shift the graph of $f$ left 9 units. 
B)  Shift the graph of f right 3 units. 
C)  Shift the graph of $f$ left 3 units. 
D)  Shift the graph of $f$ right 9 units.

Question 16

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.
-$$f ( x ) = x ^ { 3 } + 9 \text { and } g ( x ) = \sqrt [ 3 ] { x - 9 }$$

Accepted Answer

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

Question 17

Write the word or phrase that best completes each statement or answers the question.
Sketch the graph of the given function based on the graph of the function f given below.
-$$\text { Sketch the graph of } y = - f ( x + 2 ) - 1 \text {. }$$

Accepted Answer

The answer of Write the word or phrase that best...

Question 18

Determine the intervals on which the function is increasing, decreasing, and constant.
-

Accepted Answer

A)  Increasing on $( 1 , \infty )$; Decreasing on $( - \infty , 1 )$ 
B)  Increasing on $( - \infty , 1 )$; Decreasing on $( 1 , \infty )$ 
C)  Increasing on $( - \infty , - 1 )$; Decreasing on $( - 1 , \infty )$ 
D)  Increasing on $( - 1 , \infty )$; Decreasing on $( - \infty , - 1 )$ 
A)  Increasing on $( 1 , \infty )$; Decreasing on $( - \infty , 1 )$ 
B)  Increasing on $( - \infty , 1 )$; Decreasing on $( 1 , \infty )$ 
C)  Increasing on $( - \infty , - 1 )$; Decreasing on $( - 1 , \infty )$ 
D)  Increasing on $( - 1 , \infty )$; Decreasing on $( - \infty , - 1 )$

Question 19

Write the specified quantity as a function of the specified variable.
-A circle is inscribed in a square. Write the area of the square as a function of the radius.

Accepted Answer

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

Question 20

Find f(x) and g(x) so that the function can be described as y = f(g(x)).
-$$y = \sqrt { 25 x ^ { 2 } + 3 }$$

Accepted Answer

A)  $f ( x ) = \sqrt { x } , g ( x ) = 25 x ^ { 2 } + 3$ 
B)  $f ( x ) = \sqrt { 25 x ^ { 2 } } , g ( x ) = \sqrt { 3 }$ 
C)  $f ( x ) = 25 x ^ { 2 } + 3 , g ( x ) = \sqrt { x }$ 
D)  $f ( x ) = \sqrt { 25 x + 3 } , g ( x ) = x ^ { 2 }$ 
A)  $f ( x ) = \sqrt { x } , g ( x ) = 25 x ^ { 2 } + 3$ 
B)  $f ( x ) = \sqrt { 25 x ^ { 2 } } , g ( x ) = \sqrt { 3 }$ 
C)  $f ( x ) = 25 x ^ { 2 } + 3 , g ( x ) = \sqrt { x }$ 
D)  $f ( x ) = \sqrt { 25 x + 3 } , g ( x ) = x ^ { 2 }$

Identify intervals on which the function is increasing, decreasing, or constant. - $g ( x ) = 2 - ( x - 5 ) ^ { 2 }$

Tell which of the following types of regression is likely to give the most accurate model for the scatter plot shown: linear regression, quadratic regression, cubic regression, exponential regression, sinusoidal regression. -

Solve the problem. -Helen Weller invested $14,000 in an account that pays 10% simple interest. How much additional money must be invested in an account that pays 13% simple interest so that the average return on the two investments Amounts to 11%?

Identify intervals on which the function is increasing, decreasing, or constant. - $f ( x ) = | x - 7 | - 3$

Choose the one alternative that best completes the statement or answers the question. Solve the problem. - $y = ( x - 18 ) ^ { 2 }$

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

Graph the function on your calculator to determine the domain and range from the graph. - $f ( x ) = \frac { 1 } { x } + 2$

Give the equation of the function g whose graph is described. -The graph of $\mathrm { f } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } }$ is shifted $4.2$ units to the left. This graph is then vertically stretched by a factor of $3.3 .$ Finally, the graph is reflected across the $x$ -axis.

Perform the requested operation or operations. - $f ( x ) = \frac { x - 9 } { 5 } ; g ( x ) = 5 x + 9$ , find $g ( f ( x ) )$

Determine if the function is bounded above, bounded below, bounded on its domain, or unbounded on its domain. - $y = 4 ^ { - x } + 6$

Determine if the function is bounded above, bounded below, bounded on its domain, or unbounded on its domain. - $y = 30$

Describe how to transform the graph of f into the graph of g. - $f ( x ) = \sqrt { x - 3 } \text { and } g ( x ) = \sqrt { x + 6 }$

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. - $f ( x ) = x ^ { 3 } + 9 \text { and } g ( x ) = \sqrt [ 3 ] { x - 9 }$

Determine the intervals on which the function is increasing, decreasing, and constant. -

Write the specified quantity as a function of the specified variable. -A circle is inscribed in a square. Write the area of the square as a function of the radius.

Find f(x) and g(x) so that the function can be described as y = f(g(x)). - $y = \sqrt { 25 x ^ { 2 } + 3 }$

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

Identify intervals on which the function is increasing, decreasing, or constant. - g(x)=2−(x−5)2g ( x ) = 2 - ( x - 5 ) ^ { 2 }g(x)=2−(x−5)2

Write the word or phrase that best completes each statement or answers the question. Sketch the graph of the given function based on the graph of the function f given below. - Sketch the graph of y=f(3x). \text { Sketch the graph of } y = f ( 3 x ) \text {. } Sketch the graph of y=f(3x).