Question 1

Identify intervals on which the function is increasing, decreasing, or constant.
-$$h ( x ) = | x + 4 | + | x - 8 | - 9$$

Accepted Answer

A)  Increasing: $( 4 , \infty )$; decreasing: $( - \infty , 8 )$; constant: $( 4,8 )$ 
B)  Increasing: $( 8 , \infty )$; decreasing: $( - \infty , - 4 )$; constant: $( - 4,8 )$ 
C)  Increasing: $( 9 , \infty )$; decreasing: $( - \infty , 4 )$; constant: $( 4,9 )$ 
D)  Increasing: $( - \infty , - 4 )$; decreasing: $( 8 , \infty )$; constant: $( - 4,8 )$ 
A)  Increasing: $( 4 , \infty )$; decreasing: $( - \infty , 8 )$; constant: $( 4,8 )$ 
B)  Increasing: $( 8 , \infty )$; decreasing: $( - \infty , - 4 )$; constant: $( - 4,8 )$ 
C)  Increasing: $( 9 , \infty )$; decreasing: $( - \infty , 4 )$; constant: $( 4,9 )$ 
D)  Increasing: $( - \infty , - 4 )$; decreasing: $( 8 , \infty )$; constant: $( - 4,8 )$

Question 2

Identify which of the twelve basic functions listed below fit the description given.
-The four functions with local minima

Accepted Answer

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

Question 3

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

Question 4

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.
-$$y _ { 1 } = x ^ { 2 } , y _ { 2 } = - 2 ( x + 5 ) ^ { 2 } + 2$$

Accepted Answer

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

Question 5

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

Question 6

Determine if the function is one-to-one.
-

Accepted Answer

A) True 
 B)False

Question 7

Match the equation with the appropriate graph.
-$$f ( x ) = \frac { x ^ { 3 } } { x ^ { 2 } + 4 }$$

Accepted Answer

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

Question 8

Solve the problem.
-A rock is thrown vertically upward from the surface of the moon at a velocity of $32 \mathrm {~m} / \mathrm { sec }$. The graph shows the height $y$ of the rock, in meters, after $x$ seconds. Estimate and interpret the turning point (the point at which the graph reaches its maximum value).

Accepted Answer

A)  The turning point is at approximately $( 40,320 )$. This is the point at which the rock reaches its maximum height and starts to fall back towards the surface of the moon. 
B)  The turning point is at approximately $( 20,320 )$. This is the point at which the rock reaches its maximum height and starts to fall back towards the surface of the moon. 
C)  The turning point is at approximately $( 40,0 )$. This is the point at which the rock reaches the surface of the moon again. 
D)  The turning point is at approximately $( 20,320 )$. This is the point at which the rock reaches its maximum velocity and starts to slow down. 
A)  The turning point is at approximately $( 40,320 )$. This is the point at which the rock reaches its maximum height and starts to fall back towards the surface of the moon. 
B)  The turning point is at approximately $( 20,320 )$. This is the point at which the rock reaches its maximum height and starts to fall back towards the surface of the moon. 
C)  The turning point is at approximately $( 40,0 )$. This is the point at which the rock reaches the surface of the moon again. 
D)  The turning point is at approximately $( 20,320 )$. This is the point at which the rock reaches its maximum velocity and starts to slow down.

Question 9

Give the equation of the function g whose graph is described.
-The graph of $f ( x ) = x ^ { 2 } - 4 x + 3$ is horizontally shrunk by a factor of $1 / 4$.

Accepted Answer

A)  $g ( x ) = 4 x ^ { 2 } - 16 x + 12$ 
B)  $g ( x ) = \frac { 1 } { 4 } x ^ { 2 } - x + \frac { 3 } { 4 }$ 
C)  $g ( x ) = 4 x ^ { 2 } - 16 x + 3$ 
D)  $g ( x ) = \frac { 1 } { 16 } x ^ { 2 } - x + 3$ 
A)  $g ( x ) = 4 x ^ { 2 } - 16 x + 12$ 
B)  $g ( x ) = \frac { 1 } { 4 } x ^ { 2 } - x + \frac { 3 } { 4 }$ 
C)  $g ( x ) = 4 x ^ { 2 } - 16 x + 3$ 
D)  $g ( x ) = \frac { 1 } { 16 } x ^ { 2 } - x + 3$

Question 10

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

Accepted Answer

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

Question 11

Match the equation with the appropriate graph.
-$$f ( x ) = \frac { 2 x ^ { 2 } } { x ^ { 2 } - 4 }$$

Accepted Answer

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

Question 12

Identify intervals on which the function is increasing, decreasing, or constant.
-$$g ( x ) = 1.25 ( x + 8 ) ^ { 2 }$$

Accepted Answer

A)  Increasing: $( - \infty , - 8 )$; decreasing: $( - 8 , \infty )$ 
B)  Increasing: $( - 8 , \infty )$; decreasing: $( - \infty , - 8 )$ 
C)  Increasing: $( 8 , \infty )$; decreasing: $( - \infty , 8 )$ 
D)  Increasing: $( - \infty , 8 )$; decreasing: $( 8 , \infty )$ 
A)  Increasing: $( - \infty , - 8 )$; decreasing: $( - 8 , \infty )$ 
B)  Increasing: $( - 8 , \infty )$; decreasing: $( - \infty , - 8 )$ 
C)  Increasing: $( 8 , \infty )$; decreasing: $( - \infty , 8 )$ 
D)  Increasing: $( - \infty , 8 )$; decreasing: $( 8 , \infty )$

Question 13

Solve the equation graphically by converting it to an equivalent equation with 0 on the right-hand side and then finding
the x-intercepts.
-$5 x^{2}=|x|$

Accepted Answer

A)  $0 , - \frac { \sqrt { 5 } } { 5 } , \frac { \sqrt { 5 } } { 5 }$ 
B)  $0 , - \frac { 1 } { 5 } , \frac { 1 } { 5 }$ 
C)  0 
D)  $- \frac { 1 } { 5 } , \frac { 1 } { 5 }$ 
A)  $0 , - \frac { \sqrt { 5 } } { 5 } , \frac { \sqrt { 5 } } { 5 }$ 
B)  $0 , - \frac { 1 } { 5 } , \frac { 1 } { 5 }$ 
C)  0 
D)  $- \frac { 1 } { 5 } , \frac { 1 } { 5 }$

Question 14

Find two functions defined implicitly by the given relation.
-$$x ^ { 2 } - y ^ { 2 } = 100$$

Accepted Answer

A)  $y = \sqrt { x ^ { 2 } - 100 }$ or $y = \sqrt { x ^ { 2 } + 100 }$ 
B)  $y = + ( x - \sqrt { 100 } )$ or $y = - ( x - \sqrt { 100 } )$ 
C)  $y = + \sqrt { x ^ { 2 } - 100 }$ or $y = - \sqrt { x ^ { 2 } - 100 }$ 
D)  $y = x - \sqrt { 100 }$ or $y = x + \sqrt { 100 }$ 
A)  $y = \sqrt { x ^ { 2 } - 100 }$ or $y = \sqrt { x ^ { 2 } + 100 }$ 
B)  $y = + ( x - \sqrt { 100 } )$ or $y = - ( x - \sqrt { 100 } )$ 
C)  $y = + \sqrt { x ^ { 2 } - 100 }$ or $y = - \sqrt { x ^ { 2 } - 100 }$ 
D)  $y = x - \sqrt { 100 }$ or $y = x + \sqrt { 100 }$

Question 15

Find the range of the function.
-$$y = 4 x ^ { 8 }$$

Accepted Answer

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

Question 16

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.
-$$\text { Sketch the graph of } y = 1 + 2 f ( x - 1 ) \text {. }$$

Accepted Answer

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

Question 17

Find the range of the function.
-$$f ( x ) = 7 - x ^ { 2 }$$

Accepted Answer

A)  $[ - \sqrt { 7 } , \sqrt { 7 } ]$ 
B)  $[ 7 , \infty )$ 
C)  $( - \infty , \infty )$ 
D)  $( - \infty , 7 ]$ 
A)  $[ - \sqrt { 7 } , \sqrt { 7 } ]$ 
B)  $[ 7 , \infty )$ 
C)  $( - \infty , \infty )$ 
D)  $( - \infty , 7 ]$

Question 18

Perform the requested operation or operations.
-$$f ( x ) = x ^ { 2 } + 8 ; g ( x ) = \sqrt { x - 3 }$$
Find $f ( g ( x ) )$.

Accepted Answer

A)  $f ( g ( x ) ) = x + 5$ 
B)  $f ( g ( x ) ) = \frac { \sqrt { x - 3 } } { x ^ { 2 } + 8 }$ 
C)  $f ( g ( x ) ) = \left( x ^ { 2 } + 8 \right) ( \sqrt { x - 3 } )$ 
D)  $f ( g ( x ) ) = \sqrt { x ^ { 2 } + 5 }$ 
A)  $f ( g ( x ) ) = x + 5$ 
B)  $f ( g ( x ) ) = \frac { \sqrt { x - 3 } } { x ^ { 2 } + 8 }$ 
C)  $f ( g ( x ) ) = \left( x ^ { 2 } + 8 \right) ( \sqrt { x - 3 } )$ 
D)  $f ( g ( x ) ) = \sqrt { x ^ { 2 } + 5 }$

Question 19

Choose the one alternative that best completes the statement or answers the question.
Write a mathematical expression for the quantity described verbally.
-A salary after a $5.1 \%$ increase, if the original salary is x dollars

Accepted Answer

A)  $0.051 \mathrm { x }$ 
B)  $6.1 \mathrm { x }$ 
C)  $1.051 \mathrm { x }$ 
D)  $5.1 \mathrm { x }$ 
A)  $0.051 \mathrm { x }$ 
B)  $6.1 \mathrm { x }$ 
C)  $1.051 \mathrm { x }$ 
D)  $5.1 \mathrm { x }$

Question 20

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

Accepted Answer

A)  $Y e s$ 
B)  $\mathrm { No }$ 
A)  $Y e s$ 
B)  $\mathrm { No }$

Identify intervals on which the function is increasing, decreasing, or constant. - $h ( x ) = | x + 4 | + | x - 8 | - 9$

Identify which of the twelve basic functions listed below fit the description given. -The four functions with local minima

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. -

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. -

Determine if the function is one-to-one. -

Match the equation with the appropriate graph. - $f ( x ) = \frac { x ^ { 3 } } { x ^ { 2 } + 4 }$

Give the equation of the function g whose graph is described. -The graph of $f ( x ) = x ^ { 2 } - 4 x + 3$ is horizontally shrunk by a factor of $1 / 4$ .

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

Match the equation with the appropriate graph. - $f ( x ) = \frac { 2 x ^ { 2 } } { x ^ { 2 } - 4 }$

Identify intervals on which the function is increasing, decreasing, or constant. - $g ( x ) = 1.25 ( x + 8 ) ^ { 2 }$

Find two functions defined implicitly by the given relation. - $x ^ { 2 } - y ^ { 2 } = 100$

Find the range of the function. - $y = 4 x ^ { 8 }$

Find the range of the function. - $f ( x ) = 7 - x ^ { 2 }$

Perform the requested operation or operations. - $f ( x ) = x ^ { 2 } + 8 ; g ( x ) = \sqrt { x - 3 }$ Find $f ( g ( x ) )$ .

Choose the one alternative that best completes the statement or answers the question. Write a mathematical expression for the quantity described verbally. -A salary after a $5.1 \%$ increase, if the original salary is x dollars

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

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. - h(x)=∣x+4∣+∣x−8∣−9h ( x ) = | x + 4 | + | x - 8 | - 9h(x)=∣x+4∣+∣x−8∣−9

Identify which of the twelve basic functions listed below fit the description given. -The four functions with local minima

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. -

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. -

Determine if the function is one-to-one. -

Match the equation with the appropriate graph. - f(x)=x3x2+4f ( x ) = \frac { x ^ { 3 } } { x ^ { 2 } + 4 }f(x)=x2+4x3​

Give the equation of the function g whose graph is described. -The graph of f(x)=x2−4x+3f ( x ) = x ^ { 2 } - 4 x + 3f(x)=x2−4x+3 is horizontally shrunk by a factor of 1/41 / 41/4 .

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

Match the equation with the appropriate graph. - f(x)=2x2x2−4f ( x ) = \frac { 2 x ^ { 2 } } { x ^ { 2 } - 4 }f(x)=x2−42x2​

Identify intervals on which the function is increasing, decreasing, or constant. - g(x)=1.25(x+8)2g ( x ) = 1.25 ( x + 8 ) ^ { 2 }g(x)=1.25(x+8)2

Solve the equation graphically by converting it to an equivalent equation with 0 on the right-hand side and then finding the x-intercepts. - 5x2=∣x∣5 x^{2}=|x|5x2=∣x∣

Find two functions defined implicitly by the given relation. - x2−y2=100x ^ { 2 } - y ^ { 2 } = 100x2−y2=100

Find the range of the function. - y=4x8y = 4 x ^ { 8 }y=4x8

Find the range of the function. - f(x)=7−x2f ( x ) = 7 - x ^ { 2 }f(x)=7−x2

Perform the requested operation or operations. - f(x)=x2+8;g(x)=x−3f ( x ) = x ^ { 2 } + 8 ; g ( x ) = \sqrt { x - 3 }f(x)=x2+8;g(x)=x−3​ Find f(g(x))f ( g ( x ) )f(g(x)) .

Choose the one alternative that best completes the statement or answers the question. Write a mathematical expression for the quantity described verbally. -A salary after a 5.1%5.1 \%5.1% increase, if the original salary is x dollars

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

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

Identify intervals on which the function is increasing, decreasing, or constant. - $h ( x ) = | x + 4 | + | x - 8 | - 9$

Match the equation with the appropriate graph. - $f ( x ) = \frac { x ^ { 3 } } { x ^ { 2 } + 4 }$

Give the equation of the function g whose graph is described. -The graph of $f ( x ) = x ^ { 2 } - 4 x + 3$ is horizontally shrunk by a factor of $1 / 4$ .

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

Match the equation with the appropriate graph. - $f ( x ) = \frac { 2 x ^ { 2 } } { x ^ { 2 } - 4 }$

Identify intervals on which the function is increasing, decreasing, or constant. - $g ( x ) = 1.25 ( x + 8 ) ^ { 2 }$

Find two functions defined implicitly by the given relation. - $x ^ { 2 } - y ^ { 2 } = 100$

Find the range of the function. - $y = 4 x ^ { 8 }$

Find the range of the function. - $f ( x ) = 7 - x ^ { 2 }$

Perform the requested operation or operations. - $f ( x ) = x ^ { 2 } + 8 ; g ( x ) = \sqrt { x - 3 }$ Find $f ( g ( x ) )$ .

Choose the one alternative that best completes the statement or answers the question. Write a mathematical expression for the quantity described verbally. -A salary after a $5.1 \%$ increase, if the original salary is x dollars