Question 1

If $f ( x ) = \frac { 4 } { x } \text { and } g ( x ) = \frac { 4 } { x - 3 }$ find $( f \circ g ) ( 5 )$ .

Accepted Answer

2

Question 2

Graph the function. $f ( x ) = \frac { - 5 } { x + 5 } + 2$

Accepted Answer

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

Question 3

Specify the domain for the function. $h ( x ) = \frac { 1 } { ( x - 3 ) ( x + 5 ) }$

Accepted Answer

A)  $D = ( - \infty , 3 ) \cup ( 3 , \infty )$ 
B)  $D = ( - \infty , - 5 ) \cup ( - 5 , \infty )$ 
C)  $D = ( - \infty , \infty )$ 
D)  $D = ( - \infty , - 5 ) \cup ( - 5,3 ) \cup ( 3 , \infty )$ 
A)  $D = ( - \infty , 3 ) \cup ( 3 , \infty )$ 
B)  $D = ( - \infty , - 5 ) \cup ( - 5 , \infty )$ 
C)  $D = ( - \infty , \infty )$ 
D)  $D = ( - \infty , - 5 ) \cup ( - 5,3 ) \cup ( 3 , \infty )$ D

Question 4

Specify the domain for the function. Please enter your answer in interval notation. $h ( x ) = \sqrt { x + 7 }$

Accepted Answer

The answer of Specify the domain for the function. Please...

Question 5

Specify the domain for the function. Please enter your answer in interval notation. $h ( x ) = \frac { 1 } { x ^ { 2 } + 6 x - 16 }$

Accepted Answer

The answer of Specify the domain for the function. Please...

Question 6

Graph the function. $f ( x ) = - 3 \sqrt { x - 4 } + 1$

Accepted Answer

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

Question 7

Identify the graph of the function. f ( x ) = $-$ 4 x 2 $-$ 19 x $-$ 21

Accepted Answer

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

Question 8

Suppose that a car rental agency charges a fixed amount per day plus an amount per mile for renting a car. Heidi rented a car one day and paid $110.00 for 300 miles. On another day she rented a car from the same agency and paid $185.00 for 550 miles. Determine the linear function that the agency could use to determine its daily rental charges. Please enter your answer in the form f ( x ) = ax + b .

Accepted Answer

The answer of Suppose that a car rental agency charges...

Question 9

At a constant temperature, the volume ( v ) of a gas varies inversely as the pressure ( H ). Translate the statement of variation into an equation and use k as the constant of variation.

Accepted Answer

The answer of At a constant temperature, the volume (...

Question 10

Determine $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = \frac { 11 } { 8 x } \text { and } g ( x ) = \frac { 1 } { x + 5 }$

Accepted Answer

A)  $\frac { 8 x } { 11 + 40 x }$ 
B)  $\frac { 8 } { 11 - 40 x }$ 
C)  $\frac { 11 x } { 8 + 40 x }$ 
D)  $\frac { 11 + 40 x } { 8 x }$ 
A)  $\frac { 8 x } { 11 + 40 x }$ 
B)  $\frac { 8 } { 11 - 40 x }$ 
C)  $\frac { 11 x } { 8 + 40 x }$ 
D)  $\frac { 11 + 40 x } { 8 x }$

Question 11

A motel advertises that it will provide dinner, a dance, and drinks at $40 per couple for a New Year's Eve party. It must have a guarantee of 60 couples. Furthermore, it will agree that for each couple in excess of 60, it will reduce the price per couple for all attending by $0.10. How many couples will it take to maximize the motel's revenue? __________ couples

Accepted Answer

The answer of A motel advertises that it will provide...

Question 12

Suppose that a car rental agency charges a fixed amount per day plus an amount per mile for renting a car. Heidi rented a car one day and paid $60.00 for 200 miles. On another day she rented a car from the same agency and paid $90.00 for 350 miles. Determine the linear function that the agency could use to determine its daily rental charges.

Accepted Answer

A)  f ( x ) = 0.2 x + 20 
B)  f ( x ) = $-$ 0.2 x + 20 
C)  f ( x ) = 0.2 x $-$ 20 
A)  f ( x ) = 0.2 x + 20 
B)  f ( x ) = $-$ 0.2 x + 20 
C)  f ( x ) = 0.2 x $-$ 20

Question 13

Find the constant of variation for the stated condition: y is directly proportional to the square of x and inversely proportional to the cube of z , and $y = 24 \frac { 1 } { 22 }$ when x = 506 and z = 484.

Accepted Answer

The answer of Find the constant of variation for the...

Question 14

The graph of $f ( x ) = | x | - 2$ is the graph of $f ( x ) = | x |$ shifted 2 units down.

Accepted Answer

A) True 
 B)False

Question 15

Specify the domain for the function. $f ( x ) = \sqrt { x ^ { 2 } + 7 x - 18 }$

Accepted Answer

A)  $D = ( - \infty , - 9 ] \cup [ 2 , \infty )$ 
B)  $D = ( - \infty , - 2 ) \cup ( 9 , \infty )$ 
C)  $D = [ - 9,2 ]$ 
D)  $D = [ 2 , \infty )$ 
A)  $D = ( - \infty , - 9 ] \cup [ 2 , \infty )$ 
B)  $D = ( - \infty , - 2 ) \cup ( 9 , \infty )$ 
C)  $D = [ - 9,2 ]$ 
D)  $D = [ 2 , \infty )$

Question 16

Determine $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = \frac { 1 } { x } \text { and } g ( x ) = \frac { 1 } { x - 4 }$

Accepted Answer

The answer of Determine \(( g \circ f ) (...

Question 17

The linear depreciation method assumes that an item depreciates the same amount each year. Suppose a new piece of machinery costs $25,500 and it depreciates $1,750 each year for t years. Set up a linear function that yields the value of the machinery after t years. Please enter your answer in the form f ( t ) = at + b .

Accepted Answer

The answer of The linear depreciation method assumes that an...

Question 18

Determine $( g \circ f ) ( x )$ for the pair of functions f ( x ) = 7 x + 7 and g ( x ) = 6 x $-$ 5.

Accepted Answer

The answer of Determine \(( g \circ f ) (...

Question 19

Graph the function. $f ( x ) = - 3 \sqrt { x }$

Accepted Answer

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

Question 20

If y is inversely proportional to x , and $y = \frac { 1 } { 80 }$ when x = 80, find the value of y when x = 30.

Accepted Answer

A)  $y = \frac { 1 } { 26 }$ 
B)  $y = \frac { 1 } { 29 }$ 
C)  $y = \frac { 1 } { 36 }$ 
D)  $y = \frac { 1 } { 30 }$ 
E)  $y = \frac { 1 } { 40 }$ 
A)  $y = \frac { 1 } { 26 }$ 
B)  $y = \frac { 1 } { 29 }$ 
C)  $y = \frac { 1 } { 36 }$ 
D)  $y = \frac { 1 } { 30 }$ 
E)  $y = \frac { 1 } { 40 }$

If $f ( x ) = \frac { 4 } { x } \text { and } g ( x ) = \frac { 4 } { x - 3 }$ find $( f \circ g ) ( 5 )$ .

Graph the function. $f ( x ) = \frac { - 5 } { x + 5 } + 2$

Specify the domain for the function. $h ( x ) = \frac { 1 } { ( x - 3 ) ( x + 5 ) }$

Specify the domain for the function. Please enter your answer in interval notation. $h ( x ) = \sqrt { x + 7 }$

Specify the domain for the function. Please enter your answer in interval notation. $h ( x ) = \frac { 1 } { x ^ { 2 } + 6 x - 16 }$

Graph the function. $f ( x ) = - 3 \sqrt { x - 4 } + 1$

Identify the graph of the function. f ( x ) = $-$ 4 x 2 $-$ 19 x $-$ 21

At a constant temperature, the volume ( v ) of a gas varies inversely as the pressure ( H ). Translate the statement of variation into an equation and use k as the constant of variation.

Determine $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = \frac { 11 } { 8 x } \text { and } g ( x ) = \frac { 1 } { x + 5 }$

Find the constant of variation for the stated condition: y is directly proportional to the square of x and inversely proportional to the cube of z , and $y = 24 \frac { 1 } { 22 }$ when x = 506 and z = 484.

The graph of $f ( x ) = | x | - 2$ is the graph of $f ( x ) = | x |$ shifted 2 units down.

Specify the domain for the function. $f ( x ) = \sqrt { x ^ { 2 } + 7 x - 18 }$

Determine $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = \frac { 1 } { x } \text { and } g ( x ) = \frac { 1 } { x - 4 }$

Determine $( g \circ f ) ( x )$ for the pair of functions f ( x ) = 7 x + 7 and g ( x ) = 6 x $-$ 5.

Graph the function. $f ( x ) = - 3 \sqrt { x }$

If y is inversely proportional to x , and $y = \frac { 1 } { 80 }$ when x = 80, find the value of y when x = 30.

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Exponents and Polynomials

Factoring, Solving Equations and Problem Solving

A Transition From Elementary Algebra to Intermediate Algebra

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Exponential and Logarithmic Functions

Systems of Equations: Matrices and Determinants

Filters

Exam 13: Functions

If f(x)=4x and g(x)=4x−3f ( x ) = \frac { 4 } { x } \text { and } g ( x ) = \frac { 4 } { x - 3 }f(x)=x4​ and g(x)=x−34​ find (f∘g)(5)( f \circ g ) ( 5 )(f∘g)(5) .

Graph the function. f(x)=−5x+5+2f ( x ) = \frac { - 5 } { x + 5 } + 2f(x)=x+5−5​+2

Specify the domain for the function. h(x)=1(x−3)(x+5)h ( x ) = \frac { 1 } { ( x - 3 ) ( x + 5 ) }h(x)=(x−3)(x+5)1​

Specify the domain for the function. Please enter your answer in interval notation. h(x)=x+7h ( x ) = \sqrt { x + 7 }h(x)=x+7​

Specify the domain for the function. Please enter your answer in interval notation. h(x)=1x2+6x−16h ( x ) = \frac { 1 } { x ^ { 2 } + 6 x - 16 }h(x)=x2+6x−161​

Graph the function. f(x)=−3x−4+1f ( x ) = - 3 \sqrt { x - 4 } + 1f(x)=−3x−4​+1

Identify the graph of the function. f ( x ) = −-− 4 x 2 −-− 19 x −-− 21

At a constant temperature, the volume ( v ) of a gas varies inversely as the pressure ( H ). Translate the statement of variation into an equation and use k as the constant of variation.

Determine (g∘f)(x)( g \circ f ) ( x )(g∘f)(x) for the pair of functions f(x)=118x and g(x)=1x+5f ( x ) = \frac { 11 } { 8 x } \text { and } g ( x ) = \frac { 1 } { x + 5 }f(x)=8x11​ and g(x)=x+51​

Find the constant of variation for the stated condition: y is directly proportional to the square of x and inversely proportional to the cube of z , and y=24122y = 24 \frac { 1 } { 22 }y=24221​ when x = 506 and z = 484.

The graph of f(x)=∣x∣−2f ( x ) = | x | - 2f(x)=∣x∣−2 is the graph of f(x)=∣x∣f ( x ) = | x |f(x)=∣x∣ shifted 2 units down.

Specify the domain for the function. f(x)=x2+7x−18f ( x ) = \sqrt { x ^ { 2 } + 7 x - 18 }f(x)=x2+7x−18​

Determine (g∘f)(x)( g \circ f ) ( x )(g∘f)(x) for the pair of functions f(x)=1x and g(x)=1x−4f ( x ) = \frac { 1 } { x } \text { and } g ( x ) = \frac { 1 } { x - 4 }f(x)=x1​ and g(x)=x−41​

Determine (g∘f)(x)( g \circ f ) ( x )(g∘f)(x) for the pair of functions f ( x ) = 7 x + 7 and g ( x ) = 6 x −-− 5.

Graph the function. f(x)=−3xf ( x ) = - 3 \sqrt { x }f(x)=−3x​

If y is inversely proportional to x , and y=180y = \frac { 1 } { 80 }y=801​ when x = 80, find the value of y when x = 30.

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Exponents and Polynomials

Factoring, Solving Equations and Problem Solving

A Transition From Elementary Algebra to Intermediate Algebra

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Exponential and Logarithmic Functions

Systems of Equations: Matrices and Determinants

Filters

If $f ( x ) = \frac { 4 } { x } \text { and } g ( x ) = \frac { 4 } { x - 3 }$ find $( f \circ g ) ( 5 )$ .

Graph the function. $f ( x ) = \frac { - 5 } { x + 5 } + 2$

Specify the domain for the function. $h ( x ) = \frac { 1 } { ( x - 3 ) ( x + 5 ) }$

Specify the domain for the function. Please enter your answer in interval notation. $h ( x ) = \sqrt { x + 7 }$

Specify the domain for the function. Please enter your answer in interval notation. $h ( x ) = \frac { 1 } { x ^ { 2 } + 6 x - 16 }$

Graph the function. $f ( x ) = - 3 \sqrt { x - 4 } + 1$

Identify the graph of the function. f ( x ) = $-$ 4 x 2 $-$ 19 x $-$ 21

Determine $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = \frac { 11 } { 8 x } \text { and } g ( x ) = \frac { 1 } { x + 5 }$

Find the constant of variation for the stated condition: y is directly proportional to the square of x and inversely proportional to the cube of z , and $y = 24 \frac { 1 } { 22 }$ when x = 506 and z = 484.

The graph of $f ( x ) = | x | - 2$ is the graph of $f ( x ) = | x |$ shifted 2 units down.

Specify the domain for the function. $f ( x ) = \sqrt { x ^ { 2 } + 7 x - 18 }$

Determine $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = \frac { 1 } { x } \text { and } g ( x ) = \frac { 1 } { x - 4 }$

Determine $( g \circ f ) ( x )$ for the pair of functions f ( x ) = 7 x + 7 and g ( x ) = 6 x $-$ 5.

Graph the function. $f ( x ) = - 3 \sqrt { x }$

If y is inversely proportional to x , and $y = \frac { 1 } { 80 }$ when x = 80, find the value of y when x = 30.