Question 1

The composition of functions is an associative operation.

Accepted Answer

A) True 
 B)False

Question 2

Specify the domain of $( g \circ f ) ( x )$ for the pair of functions f ( x ) = 7 x + 3 and g ( x ) = x 2 + 5. Please enter your answer in interval notation.

Accepted Answer

The answer of Specify the domain of \(( g \circ...

Question 3

Specify the domain for the relation. {(4, 2), (8, 5), (13, 12), (16, 17)}

Accepted Answer

A)  D = {4, 8, 13, 16, 2, 5, 12, 17} 
B)  D = {4, 8, 13, 16} 
C)  D = ( $-$ 4, 16) 
D)  D = {2, 5, 12, 17} 
A)  D = {4, 8, 13, 16, 2, 5, 12, 17} 
B)  D = {4, 8, 13, 16} 
C)  D = ( $-$ 4, 16) 
D)  D = {2, 5, 12, 17}

Question 4

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

Accepted Answer

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

Question 5

The graph of $f ( x ) = \frac { 1 } { x + 3 }$ has a vertical translation with respect to the graph $f ( x ) = \frac { 1 } { x }$ .

Accepted Answer

A) True 
 B)False

Question 6

Find the constant of variation for the stated condition: y varies directly as x and inversely as z , and y = 180 when x = 279 and z = 31.

Accepted Answer

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

Question 7

Specify the domain of $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = \frac { 3 } { 2 x } \text { and } g ( x ) = \frac { 1 } { x + 6 }$

Accepted Answer

A)  $( - \infty , - 6 ) \cup ( - 6 , \infty )$ 
B)  $( - \infty , 0 ) \cup ( 0 , \infty )$ 
C)  $( - \infty , - 6 ) \cup ( 0 , \infty )$ 
D)  $( - \infty , - 6 ) \cup ( - 6,0 ) \cup ( 0 , \infty )$ 
A)  $( - \infty , - 6 ) \cup ( - 6 , \infty )$ 
B)  $( - \infty , 0 ) \cup ( 0 , \infty )$ 
C)  $( - \infty , - 6 ) \cup ( 0 , \infty )$ 
D)  $( - \infty , - 6 ) \cup ( - 6,0 ) \cup ( 0 , \infty )$

Question 8

Specify the domain for the function. Please enter your answer in interval notation. $h ( x ) = \frac { 1 } { ( x - 4 ) ( x + 8 ) }$

Accepted Answer

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

Question 9

The volume ( Z ) of a gas varies directly as the absolute temperature ( Q ) and 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 The volume ( Z ) of a...

Question 10

Zack wants to sell five items that cost him $1.50, $2.70, $5.20, $13.00, and $17.70. He wants to make a profit of 70% of the cost. Create a function that you can use to determine the selling price of each item, and then use the function to calculate each selling price.

Accepted Answer

A)  Item 1 Item 2 Item 3 Item 4 Item 5 Cost $1.50 $2.70 $5.20 $13.00 $17.70 Selling price $4.05 $7.29 $14.04 $35.10 $47.79 
B)  Item 1 Item 2 Item 3 Item 4 Item 5 Cost $1.50 $2.70 $5.20 $13.00 $17.70 Selling price $2.55 $4.59 $8.84 $22.10 $30.09 
C)  Item 1 Item 2 Item 3 Item 4 Item 5 Cost $1.50 $2.70 $5.20 $13.00 $17.70 Selling price $1.05 $1.89 $3.64 $9.10 $12.39 
A)  Item 1 Item 2 Item 3 Item 4 Item 5 Cost $1.50 $2.70 $5.20 $13.00 $17.70 Selling price $4.05 $7.29 $14.04 $35.10 $47.79 
B)  Item 1 Item 2 Item 3 Item 4 Item 5 Cost $1.50 $2.70 $5.20 $13.00 $17.70 Selling price $2.55 $4.59 $8.84 $22.10 $30.09 
C)  Item 1 Item 2 Item 3 Item 4 Item 5 Cost $1.50 $2.70 $5.20 $13.00 $17.70 Selling price $1.05 $1.89 $3.64 $9.10 $12.39

Question 11

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

Accepted Answer

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

Question 12

The period (the time required for one complete oscillation) of a simple pendulum varies directly as the square root of its length. If a pendulum 1 inches long has a period of 0.5 seconds, find the period of a pendulum 9 inches long. Express your answer to the nearest tenth of a second.

Accepted Answer

A)  P = 3.5 seconds 
B)  P = 1.3 seconds 
C)  P = 2.0 seconds 
D)  P = 1.2 seconds 
E)  P = 1.5 seconds 
A)  P = 3.5 seconds 
B)  P = 1.3 seconds 
C)  P = 2.0 seconds 
D)  P = 1.2 seconds 
E)  P = 1.5 seconds

Question 13

The linear depreciation method assumes that an item depreciates the same amount each year. Suppose a new piece of machinery costs $32,000 and it depreciates $1,650 each year for t years. Set up a linear function that yields the value of the machinery after t years.

Accepted Answer

A)  f ( t ) = 32,000 $-$ 1,650 t 
B)  f ( t ) = 1,650 t + 32,000 
C)  f ( t ) = 1,650 t $-$ 32,000 
A)  f ( t ) = 32,000 $-$ 1,650 t 
B)  f ( t ) = 1,650 t + 32,000 
C)  f ( t ) = 1,650 t $-$ 32,000

Question 14

Determine $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = \sqrt { x } \text { and } g ( x ) = \frac { 7 } { x }$ .

Accepted Answer

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

Question 15

The graph of a quadratic equation is a parabola.

Accepted Answer

A) True 
 B)False

Question 16

Specify the domain for the function. Please enter your answer in interval notation. $f ( t ) = \frac { - 6 } { x ^ { 2 } + 8 }$

Accepted Answer

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

Question 17

Determine $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = \frac { 4 } { x } \text { and } g ( x ) = 5 x - 5$

Accepted Answer

A)  20 x $-$ 5 
B)  $\frac { 4 } { x } + 5$ 
C)  $\frac { 4 } { 5 x - 5 }$ 
D)  $\frac { 20 } { x } - 5$ 
A)  20 x $-$ 5 
B)  $\frac { 4 } { x } + 5$ 
C)  $\frac { 4 } { 5 x - 5 }$ 
D)  $\frac { 20 } { x } - 5$

Question 18

Find $\frac { f ( a + h ) - f ( a ) } { h }$ for f ( x ) = x 2 $-$ 8 x + 2.

Accepted Answer

The answer of Find \(\frac { f ( a +...

Question 19

The linear depreciation method assumes that an item depreciates the same amount each year. Suppose a new piece of machinery costs $22,500 and it depreciates $1,450 each year for t years. Find the value of the machinery after 8 years.

Accepted Answer

A)  $11,600 
B)  $34,100 
C)  $10,900 
A)  $11,600 
B)  $34,100 
C)  $10,900

Question 20

Determine $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = \sqrt { x + 3 } \text { and } g ( x ) = 8 x + 7$ .

Accepted Answer

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

The composition of functions is an associative operation.

Specify the domain of $( g \circ f ) ( x )$ for the pair of functions f ( x ) = 7 x + 3 and g ( x ) = x 2 + 5. Please enter your answer in interval notation.

Specify the domain for the relation. {(4, 2), (8, 5), (13, 12), (16, 17)}

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

The graph of $f ( x ) = \frac { 1 } { x + 3 }$ has a vertical translation with respect to the graph $f ( x ) = \frac { 1 } { x }$ .

Find the constant of variation for the stated condition: y varies directly as x and inversely as z , and y = 180 when x = 279 and z = 31.

Specify the domain of $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = \frac { 3 } { 2 x } \text { and } g ( x ) = \frac { 1 } { x + 6 }$

Specify the domain for the function. Please enter your answer in interval notation. $h ( x ) = \frac { 1 } { ( x - 4 ) ( x + 8 ) }$

The volume ( Z ) of a gas varies directly as the absolute temperature ( Q ) and inversely as the pressure ( H ). Translate the statement of variation into an equation and use k as the constant of variation.

Zack wants to sell five items that cost him $1.50, $2.70, $5.20, $13.00, and $17.70. He wants to make a profit of 70% of the cost. Create a function that you can use to determine the selling price of each item, and then use the function to calculate each selling price.

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

The period (the time required for one complete oscillation) of a simple pendulum varies directly as the square root of its length. If a pendulum 1 inches long has a period of 0.5 seconds, find the period of a pendulum 9 inches long. Express your answer to the nearest tenth of a second.

The linear depreciation method assumes that an item depreciates the same amount each year. Suppose a new piece of machinery costs $32,000 and it depreciates $1,650 each year for t years. Set up a linear function that yields the value of the machinery after t years.

Determine $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = \sqrt { x } \text { and } g ( x ) = \frac { 7 } { x }$ .

The graph of a quadratic equation is a parabola.

Specify the domain for the function. Please enter your answer in interval notation. $f ( t ) = \frac { - 6 } { x ^ { 2 } + 8 }$

Determine $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = \frac { 4 } { x } \text { and } g ( x ) = 5 x - 5$

Find $\frac { f ( a + h ) - f ( a ) } { h }$ for f ( x ) = x 2 $-$ 8 x + 2.

The linear depreciation method assumes that an item depreciates the same amount each year. Suppose a new piece of machinery costs $22,500 and it depreciates $1,450 each year for t years. Find the value of the machinery after 8 years.

Determine $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = \sqrt { x + 3 } \text { and } g ( x ) = 8 x + 7$ .

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

The composition of functions is an associative operation.

Specify the domain of (g∘f)(x)( g \circ f ) ( x )(g∘f)(x) for the pair of functions f ( x ) = 7 x + 3 and g ( x ) = x 2 + 5. Please enter your answer in interval notation.

Specify the domain for the relation. {(4, 2), (8, 5), (13, 12), (16, 17)}

Graph the function. f(x)=1x−2f ( x ) = \frac { 1 } { x } - 2f(x)=x1​−2

The graph of f(x)=1x+3f ( x ) = \frac { 1 } { x + 3 }f(x)=x+31​ has a vertical translation with respect to the graph f(x)=1xf ( x ) = \frac { 1 } { x }f(x)=x1​ .

Find the constant of variation for the stated condition: y varies directly as x and inversely as z , and y = 180 when x = 279 and z = 31.

Specify the domain of (g∘f)(x)( g \circ f ) ( x )(g∘f)(x) for the pair of functions f(x)=32x and g(x)=1x+6f ( x ) = \frac { 3 } { 2 x } \text { and } g ( x ) = \frac { 1 } { x + 6 }f(x)=2x3​ and g(x)=x+61​

Specify the domain for the function. Please enter your answer in interval notation. h(x)=1(x−4)(x+8)h ( x ) = \frac { 1 } { ( x - 4 ) ( x + 8 ) }h(x)=(x−4)(x+8)1​

The volume ( Z ) of a gas varies directly as the absolute temperature ( Q ) and inversely as the pressure ( H ). Translate the statement of variation into an equation and use k as the constant of variation.

Zack wants to sell five items that cost him $1.50, $2.70, $5.20, $13.00, and $17.70. He wants to make a profit of 70% of the cost. Create a function that you can use to determine the selling price of each item, and then use the function to calculate each selling price.

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

The period (the time required for one complete oscillation) of a simple pendulum varies directly as the square root of its length. If a pendulum 1 inches long has a period of 0.5 seconds, find the period of a pendulum 9 inches long. Express your answer to the nearest tenth of a second.

The linear depreciation method assumes that an item depreciates the same amount each year. Suppose a new piece of machinery costs $32,000 and it depreciates $1,650 each year for t years. Set up a linear function that yields the value of the machinery after t years.

Determine (g∘f)(x)( g \circ f ) ( x )(g∘f)(x) for the pair of functions f(x)=x and g(x)=7xf ( x ) = \sqrt { x } \text { and } g ( x ) = \frac { 7 } { x }f(x)=x​ and g(x)=x7​ .

The graph of a quadratic equation is a parabola.

Specify the domain for the function. Please enter your answer in interval notation. f(t)=−6x2+8f ( t ) = \frac { - 6 } { x ^ { 2 } + 8 }f(t)=x2+8−6​

Determine (g∘f)(x)( g \circ f ) ( x )(g∘f)(x) for the pair of functions f(x)=4x and g(x)=5x−5f ( x ) = \frac { 4 } { x } \text { and } g ( x ) = 5 x - 5f(x)=x4​ and g(x)=5x−5

Find f(a+h)−f(a)h\frac { f ( a + h ) - f ( a ) } { h }hf(a+h)−f(a)​ for f ( x ) = x 2 −-− 8 x + 2.

The linear depreciation method assumes that an item depreciates the same amount each year. Suppose a new piece of machinery costs $22,500 and it depreciates $1,450 each year for t years. Find the value of the machinery after 8 years.

Determine (g∘f)(x)( g \circ f ) ( x )(g∘f)(x) for the pair of functions f(x)=x+3 and g(x)=8x+7f ( x ) = \sqrt { x + 3 } \text { and } g ( x ) = 8 x + 7f(x)=x+3​ and g(x)=8x+7 .

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

Specify the domain of $( g \circ f ) ( x )$ for the pair of functions f ( x ) = 7 x + 3 and g ( x ) = x 2 + 5. Please enter your answer in interval notation.

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

The graph of $f ( x ) = \frac { 1 } { x + 3 }$ has a vertical translation with respect to the graph $f ( x ) = \frac { 1 } { x }$ .

Specify the domain of $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = \frac { 3 } { 2 x } \text { and } g ( x ) = \frac { 1 } { x + 6 }$

Specify the domain for the function. Please enter your answer in interval notation. $h ( x ) = \frac { 1 } { ( x - 4 ) ( x + 8 ) }$

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

Determine $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = \sqrt { x } \text { and } g ( x ) = \frac { 7 } { x }$ .

Specify the domain for the function. Please enter your answer in interval notation. $f ( t ) = \frac { - 6 } { x ^ { 2 } + 8 }$

Determine $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = \frac { 4 } { x } \text { and } g ( x ) = 5 x - 5$

Find $\frac { f ( a + h ) - f ( a ) } { h }$ for f ( x ) = x 2 $-$ 8 x + 2.

Determine $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = \sqrt { x + 3 } \text { and } g ( x ) = 8 x + 7$ .