Question 1

Evaluate the function.
-Find $f ( 0 )$ when $f ( x ) = x ^ { 2 } + 5 x - 7$

Accepted Answer

A)  7 
B)  0 
C)  $- 7$ 
D)  49 
A)  7 
B)  0 
C)  $- 7$ 
D)  49

Question 2

Write an equation for the line described. Give your answer in slope-intercept form.
-through $( - 7 , - 2 )$ and $( 0,2 )$

Accepted Answer

A)  $y = - \frac { 4 } { 7 } x + 2$ 
B)  $y = - \frac { 5 } { 2 } x + 2$ 
C)  $y = \frac { 4 } { 7 } x + 2$ 
D)  $y = \frac { 5 } { 2 } x + 2$ 
A)  $y = - \frac { 4 } { 7 } x + 2$ 
B)  $y = - \frac { 5 } { 2 } x + 2$ 
C)  $y = \frac { 4 } { 7 } x + 2$ 
D)  $y = \frac { 5 } { 2 } x + 2$

Question 3

Describe the transformations and give the equation for the graph.
-

Accepted Answer

A)  It is the graph of $f ( x ) = \sqrt { x }$ translated 5 units to the right, shrunken vertically by a factor of $\frac { 1 } { 3 }$ and translated 4 units up. The equation is $y = \frac { 1 } { 3 } \sqrt { x + 5 } + 4$ 
B)  It is the graph of $f ( x ) = \sqrt { x }$ translated 5 units to the right, shrunken vertically by a factor of $\frac { 1 } { 3 }$ and translated 4 units up. The equation is $\mathrm { y } = \frac { 1 } { 3 } \sqrt { \mathrm { x } - 5 } + 4$ 
C)  It is the graph of $f ( x ) = \sqrt { x }$ translated 5 units to the right, stretched vertically by a factor of 3 and translated 4 units up. The equation is $y = 3 \sqrt { x + 5 } + 4$ 
D)  It is the graph of $f ( x ) = \sqrt { x }$ translated 5 units to the right, stretched vertically by a factor of 3 and translated 4 units up. The equation is $y = 3 \sqrt { x - 5 } + 4$ 
A)  It is the graph of $f ( x ) = \sqrt { x }$ translated 5 units to the right, shrunken vertically by a factor of $\frac { 1 } { 3 }$ and translated 4 units up. The equation is $y = \frac { 1 } { 3 } \sqrt { x + 5 } + 4$ 
B)  It is the graph of $f ( x ) = \sqrt { x }$ translated 5 units to the right, shrunken vertically by a factor of $\frac { 1 } { 3 }$ and translated 4 units up. The equation is $\mathrm { y } = \frac { 1 } { 3 } \sqrt { \mathrm { x } - 5 } + 4$ 
C)  It is the graph of $f ( x ) = \sqrt { x }$ translated 5 units to the right, stretched vertically by a factor of 3 and translated 4 units up. The equation is $y = 3 \sqrt { x + 5 } + 4$ 
D)  It is the graph of $f ( x ) = \sqrt { x }$ translated 5 units to the right, stretched vertically by a factor of 3 and translated 4 units up. The equation is $y = 3 \sqrt { x - 5 } + 4$

Question 4

Solve the problem.
-Select the equation that describes the graph shown.

Accepted Answer

A)  $y = - 2 x ^ { 2 } - 5$ 
B)  $y = - 2 ( x - 5 ) ^ { 2 } + 2$ 
C)  $y = - 2 ( x + 5 ) ^ { 2 }$ 
D)  $y = - 2 ( x - 5 ) ^ { 2 }$ 
A)  $y = - 2 x ^ { 2 } - 5$ 
B)  $y = - 2 ( x - 5 ) ^ { 2 } + 2$ 
C)  $y = - 2 ( x + 5 ) ^ { 2 }$ 
D)  $y = - 2 ( x - 5 ) ^ { 2 }$

Question 5

Solve the problem.
-Employees of a publishing company received an increase in salary of 5% plus a bonus of $700. Let S(x) represent the new salary in terms of the previous salary x. Find the value of S(12,000).

Accepted Answer

A)  $13,300 
B)  $18,700 
C)  $12,700 
D)  $10,762 
A)  $13,300 
B)  $18,700 
C)  $12,700 
D)  $10,762

Question 6

Graph the function.
-$$f ( x ) = - \frac { 1 } { 3 } x ^ { 2 }$$

Accepted Answer

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

Question 7

Give the domain and range of the relation.
-

Accepted Answer

A)  range: $( - \infty , 0 ) \cup ( 0,4 ) \cup ( 4 , \infty )$; domain: $( - \infty , - 5 ) \cup ( - 5,0 ) \cup ( 0 , \infty )$ 
B)  range: $( - \infty , \infty )$; domain: $( - \infty , \infty )$ 
C)  range: $( - \infty , 4 ) \cup ( 4 , \infty )$; domain: $( - \infty , - 5 ) \cup ( - 5 , \infty )$ 
D)  None of these 
A)  range: $( - \infty , 0 ) \cup ( 0,4 ) \cup ( 4 , \infty )$; domain: $( - \infty , - 5 ) \cup ( - 5,0 ) \cup ( 0 , \infty )$ 
B)  range: $( - \infty , \infty )$; domain: $( - \infty , \infty )$ 
C)  range: $( - \infty , 4 ) \cup ( 4 , \infty )$; domain: $( - \infty , - 5 ) \cup ( - 5 , \infty )$ 
D)  None of these

Question 8

Evaluate.
-Find $\left( \frac { f } { g } \right) ( - 3 )$ when $f ( x ) = 2 x - 5$ and $g ( x ) = 5 x ^ { 2 } + 14 x + 2$

Accepted Answer

A)  $- \frac { 11 } { 5 }$ 
B)  $\frac { 2 } { 5 }$ 
C)  1 
D)  5 
A)  $- \frac { 11 } { 5 }$ 
B)  $\frac { 2 } { 5 }$ 
C)  1 
D)  5

Question 9

Graph the function.
-$$f ( x ) = \frac { 1 } { 5 } | - x |$$

Accepted Answer

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

Question 10

For the pair of functions, find the indicated sum, difference, product, or quotient.
-$$f ( x ) = \sqrt { 8 x - 4 } , g ( x ) = \frac { 1 } { x }$$
Find $( f - g ) ( x )$.

Accepted Answer

A)  $\frac { 1 } { \sqrt { 8 x - 4 } - x }$ 
B)  $\sqrt { 8 x - 4 } - \frac { 1 } { x }$ 
C)  $\frac { 1 } { x } - \sqrt { 8 x - 4 }$ 
D)  $\sqrt { 8 x - 4 - \frac { 1 } { x } }$ 
A)  $\frac { 1 } { \sqrt { 8 x - 4 } - x }$ 
B)  $\sqrt { 8 x - 4 } - \frac { 1 } { x }$ 
C)  $\frac { 1 } { x } - \sqrt { 8 x - 4 }$ 
D)  $\sqrt { 8 x - 4 - \frac { 1 } { x } }$

Question 11

Solve the problem.
-Assume it costs 25 cents to mail a letter weighing one ounce or less, and then 20 cents for each additional ounce or fraction of an ounce. Let L(x) be the cost of mailing a letter weighing x ounces. $$\text { Graph } y = L ( x ) \text {. }$$

Accepted Answer

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

Question 12

Graph the function.
-$$f ( x ) = 2 ( x + 1 ) ^ { 2 } + 4$$

Accepted Answer

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

Question 13

Decide whether the relation defines a function.
-

Accepted Answer

A)  Function 
B)  Not a function 
A)  Function 
B)  Not a function

Question 14

The figure below shows the graph of a function y = f(x). Use this graph to solve the problem.
-$$\text { Sketch the graph of } y = - f ( x ) \text {. }$$

Accepted Answer

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

Question 15

Solve the problem.
-The volume of water added to a circular drum of radius $r$ is given by $V _ { W } = 20 t$, where $V _ { W }$ is volume in $\mathrm { cu } \mathrm {} \mathrm { ft }$ and $\mathrm { t }$ is time in sec. Find the depth of water in a drum of radius $4 \mathrm { ft }$ after adding water for $10 \mathrm { sec }$. (Round result to one decimal place.)

Accepted Answer

A)  $12.6 \mathrm { ft }$ 
B)  $4.0 \mathrm { ft }$ 
C)  $8.0 \mathrm { ft }$ 
D)  $2.0 \mathrm { ft }$ 
A)  $12.6 \mathrm { ft }$ 
B)  $4.0 \mathrm { ft }$ 
C)  $8.0 \mathrm { ft }$ 
D)  $2.0 \mathrm { ft }$

Question 16

Solve the problem.
-The graphs of functions $\mathrm { f }$ and $g$ are shown. Use these graphs to find (fg)(1).

Accepted Answer

A)  2 
B)  $- 4$ 
C)  3 
D)  $- 3$ 
A)  2 
B)  $- 4$ 
C)  3 
D)  $- 3$

Question 17

Decide whether the relation defines a function.
-$$5 x = 9 - 7 y$$

Accepted Answer

A)  Function 
B)  Not a function 
A)  Function 
B)  Not a function

Question 18

Solve the problem.
-Select the equation that describes the graph shown.

Accepted Answer

A)  $y = ( x + 1 ) ^ { 2 } + 2$ 
B)  $y = x ^ { 2 } - 1$ 
C)  $\mathrm { y } = ( \mathrm { x } - 1 ) ^ { 2 } + 2$ 
D)  $y = ( x + 2 ) ^ { 2 } - 1$ 
A)  $y = ( x + 1 ) ^ { 2 } + 2$ 
B)  $y = x ^ { 2 } - 1$ 
C)  $\mathrm { y } = ( \mathrm { x } - 1 ) ^ { 2 } + 2$ 
D)  $y = ( x + 2 ) ^ { 2 } - 1$

Question 19

Find the specified domain.
-Find the domain of $( f + g ) ( x )$ when $f ( x ) = 2 x + 3$ and $g ( x ) = \frac { 3 } { x - 8 }$

Accepted Answer

A)  $( - \infty , \infty )$ 
B)  $( - \infty , 8 ) \cup ( 8 , \infty )$ 
C)  $( - \infty , - 8 ) \cup ( - 8 , \infty )$ 
D)  $( - \infty , - 3 ) \cup ( - 3 , \infty )$ 
A)  $( - \infty , \infty )$ 
B)  $( - \infty , 8 ) \cup ( 8 , \infty )$ 
C)  $( - \infty , - 8 ) \cup ( - 8 , \infty )$ 
D)  $( - \infty , - 3 ) \cup ( - 3 , \infty )$

Question 20

Find the center-radius form of the circle described or graphed.
-

Accepted Answer

A)  $( x - 6 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 4$ 
B)  $( x + 6 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 2$ 
C)  $( x + 6 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 4$ 
D)  $( x - 6 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 2$ 
A)  $( x - 6 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 4$ 
B)  $( x + 6 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 2$ 
C)  $( x + 6 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 4$ 
D)  $( x - 6 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 2$

Evaluate the function. -Find $f ( 0 )$ when $f ( x ) = x ^ { 2 } + 5 x - 7$

Write an equation for the line described. Give your answer in slope-intercept form. -through $( - 7 , - 2 )$ and $( 0,2 )$

Describe the transformations and give the equation for the graph. -

Solve the problem. -Select the equation that describes the graph shown.

Solve the problem. -Employees of a publishing company received an increase in salary of 5% plus a bonus of $700. Let S(x) represent the new salary in terms of the previous salary x. Find the value of S(12,000).

Graph the function. - $f ( x ) = - \frac { 1 } { 3 } x ^ { 2 }$ $Graph the function. - f ( x ) = - \frac { 1 } { 3 } x ^ { 2 }$

Give the domain and range of the relation. -

Evaluate. -Find $\left( \frac { f } { g } \right) ( - 3 )$ when $f ( x ) = 2 x - 5$ and $g ( x ) = 5 x ^ { 2 } + 14 x + 2$

Graph the function. - $f ( x ) = \frac { 1 } { 5 } | - x |$ $Graph the function. - f ( x ) = \frac { 1 } { 5 } | - x |$

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = \sqrt { 8 x - 4 } , g ( x ) = \frac { 1 } { x }$ Find $( f - g ) ( x )$ .

Graph the function. - $f ( x ) = 2 ( x + 1 ) ^ { 2 } + 4$ $Graph the function. - f ( x ) = 2 ( x + 1 ) ^ { 2 } + 4$

Decide whether the relation defines a function. -

Solve the problem. -The graphs of functions $\mathrm { f }$ and $g$ are shown. Use these graphs to find (fg)(1). $Solve the problem. -The graphs of functions \mathrm { f } and g are shown. Use these graphs to find (fg)(1).$

Decide whether the relation defines a function. - $5 x = 9 - 7 y$

Solve the problem. -Select the equation that describes the graph shown.

Find the specified domain. -Find the domain of $( f + g ) ( x )$ when $f ( x ) = 2 x + 3$ and $g ( x ) = \frac { 3 } { x - 8 }$

Find the center-radius form of the circle described or graphed. -

Equations and Inequalities

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Exam 2: Graphs and Functions

Evaluate the function. -Find f(0)f ( 0 )f(0) when f(x)=x2+5x−7f ( x ) = x ^ { 2 } + 5 x - 7f(x)=x2+5x−7

Write an equation for the line described. Give your answer in slope-intercept form. -through (−7,−2)( - 7 , - 2 )(−7,−2) and (0,2)( 0,2 )(0,2)

Describe the transformations and give the equation for the graph. -

Solve the problem. -Select the equation that describes the graph shown.

Solve the problem. -Employees of a publishing company received an increase in salary of 5% plus a bonus of $700. Let S(x) represent the new salary in terms of the previous salary x. Find the value of S(12,000).

Graph the function. - f(x)=−13x2f ( x ) = - \frac { 1 } { 3 } x ^ { 2 }f(x)=−31​x2

Give the domain and range of the relation. -

Evaluate. -Find (fg)(−3)\left( \frac { f } { g } \right) ( - 3 )(gf​)(−3) when f(x)=2x−5f ( x ) = 2 x - 5f(x)=2x−5 and g(x)=5x2+14x+2g ( x ) = 5 x ^ { 2 } + 14 x + 2g(x)=5x2+14x+2

Graph the function. - f(x)=15∣−x∣f ( x ) = \frac { 1 } { 5 } | - x |f(x)=51​∣−x∣

For the pair of functions, find the indicated sum, difference, product, or quotient. - f(x)=8x−4,g(x)=1xf ( x ) = \sqrt { 8 x - 4 } , g ( x ) = \frac { 1 } { x }f(x)=8x−4​,g(x)=x1​ Find (f−g)(x)( f - g ) ( x )(f−g)(x) .

Solve the problem. -Assume it costs 25 cents to mail a letter weighing one ounce or less, and then 20 cents for each additional ounce or fraction of an ounce. Let L(x) be the cost of mailing a letter weighing x ounces. Graph y=L(x). \text { Graph } y = L ( x ) \text {. } Graph y=L(x).

Graph the function. - f(x)=2(x+1)2+4f ( x ) = 2 ( x + 1 ) ^ { 2 } + 4f(x)=2(x+1)2+4

Decide whether the relation defines a function. -

The figure below shows the graph of a function y = f(x). Use this graph to solve the problem. - Sketch the graph of y=−f(x). \text { Sketch the graph of } y = - f ( x ) \text {. } Sketch the graph of y=−f(x).

Solve the problem. -The graphs of functions f\mathrm { f }f and ggg are shown. Use these graphs to find (fg)(1).

Decide whether the relation defines a function. - 5x=9−7y5 x = 9 - 7 y5x=9−7y

Solve the problem. -Select the equation that describes the graph shown.

Find the specified domain. -Find the domain of (f+g)(x)( f + g ) ( x )(f+g)(x) when f(x)=2x+3f ( x ) = 2 x + 3f(x)=2x+3 and g(x)=3x−8g ( x ) = \frac { 3 } { x - 8 }g(x)=x−83​

Find the center-radius form of the circle described or graphed. -

Equations and Inequalities

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Evaluate the function. -Find $f ( 0 )$ when $f ( x ) = x ^ { 2 } + 5 x - 7$

Write an equation for the line described. Give your answer in slope-intercept form. -through $( - 7 , - 2 )$ and $( 0,2 )$

Graph the function. - $f ( x ) = - \frac { 1 } { 3 } x ^ { 2 }$ $Graph the function. - f ( x ) = - \frac { 1 } { 3 } x ^ { 2 }$

Evaluate. -Find $\left( \frac { f } { g } \right) ( - 3 )$ when $f ( x ) = 2 x - 5$ and $g ( x ) = 5 x ^ { 2 } + 14 x + 2$

Graph the function. - $f ( x ) = \frac { 1 } { 5 } | - x |$ $Graph the function. - f ( x ) = \frac { 1 } { 5 } | - x |$

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = \sqrt { 8 x - 4 } , g ( x ) = \frac { 1 } { x }$ Find $( f - g ) ( x )$ .

Graph the function. - $f ( x ) = 2 ( x + 1 ) ^ { 2 } + 4$ $Graph the function. - f ( x ) = 2 ( x + 1 ) ^ { 2 } + 4$

Solve the problem. -The graphs of functions $\mathrm { f }$ and $g$ are shown. Use these graphs to find (fg)(1). $Solve the problem. -The graphs of functions \mathrm { f } and g are shown. Use these graphs to find (fg)(1).$

Decide whether the relation defines a function. - $5 x = 9 - 7 y$

Find the specified domain. -Find the domain of $( f + g ) ( x )$ when $f ( x ) = 2 x + 3$ and $g ( x ) = \frac { 3 } { x - 8 }$