Exam 13: Functions

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

(Multiple Choice)

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Question 141

Graph the function. $f ( x ) = - 4 | x |$

(Multiple Choice)

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Question 142

For each of the quadratic functions find its graph. Match each function with the corresponding graph. -

(Multiple Choice)

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Question 143

Specify the domain for the function. $h ( x ) = \frac { 1 } { x ^ { 2 } + 4 x - 32 }$

(Multiple Choice)

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Question 144

Specify the range for the following relation. Please enter your answer in interval notation. {( x , y ) | 5 x ² = 8 y ³}

(Short Answer)

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Question 145

Specify the domain for the function. $f ( t ) = \frac { - 2 } { x ^ { 2 } + 3 }$

(Multiple Choice)

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Question 146

Find the constant of variation for the stated condition: y varies directly as x and inversely as z , and y = 20 when x = 170 and z = 34.

(Multiple Choice)

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Question 147

The simple interest earned by a certain amount of money varies jointly as the rate of interest and the time (in years) that the money is invested. If the money is invested at 14% for 2 years, $84 is earned. How much is earned if the money is invested at 15% for 4 years? $__________

(Short Answer)

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Question 148

A motel advertises that it will provide dinner, a dance, and drinks at $30 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 $0.50. How many couples will it take to maximize the motel's revenue?

(Multiple Choice)

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Question 149

Find the constant of variation for the stated condition: y varies directly as x , and y = 125 when x = 100. Please enter your answer as a fraction.

(Short Answer)

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Question 150

For each of the linear functions find its graph. Match each function with the corresponding graph. -

(Multiple Choice)

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Question 151

Find the constant of variation for the stated condition: r varies inversely as the cube of t , and $r = \frac { 1 } { 81 }$ when t = 9.

(Short Answer)

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Question 152

If $f ( x ) = - \frac { 5 } { x + 1 }$ find $f ( - 6 ) , f ( 0 ) , f ( - 1 ) , f ( 4 )$ .

(Short Answer)

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Question 153

If g ( x ) = 4 x + 3 and f ( x ) = 5 x 2 $-$ 9, find $( g \circ f ) ( 3 )$ .

(Multiple Choice)

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Question 154

Specify the domain for the following relation. Please enter your answer in interval notation. {( x , y ) | 9 y $-$ 7 x = 15}

(Short Answer)

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Question 155

Graph the function. $f ( x ) = - 2 ( x - 1 ) ^ { 2 } - 6$

(Multiple Choice)

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Question 156

Graph the function. $f ( x ) = \sqrt { 7 - x }$

(Multiple Choice)

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Question 157

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

(Multiple Choice)

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Question 158

Identify the graph of the function. f ( x ) = $-$ 3 x 2 $-$ 8 x

(Multiple Choice)

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Question 159

Identify the graph of the function. f ( x ) = x 2 $-$ 3 x $-$ 1

(Multiple Choice)

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Question 160

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

Graph the function. $f ( x ) = - 4 | x |$

For each of the quadratic functions find its graph. Match each function with the corresponding graph. -

Specify the domain for the function. $h ( x ) = \frac { 1 } { x ^ { 2 } + 4 x - 32 }$

Specify the range for the following relation. Please enter your answer in interval notation. {( x , y ) | 5 x ² = 8 y ³}

Specify the domain for the function. $f ( t ) = \frac { - 2 } { x ^ { 2 } + 3 }$

Find the constant of variation for the stated condition: y varies directly as x and inversely as z , and y = 20 when x = 170 and z = 34.

The simple interest earned by a certain amount of money varies jointly as the rate of interest and the time (in years) that the money is invested. If the money is invested at 14% for 2 years, $84 is earned. How much is earned if the money is invested at 15% for 4 years? $__________

Find the constant of variation for the stated condition: y varies directly as x , and y = 125 when x = 100. Please enter your answer as a fraction.

For each of the linear functions find its graph. Match each function with the corresponding graph. -

Find the constant of variation for the stated condition: r varies inversely as the cube of t , and $r = \frac { 1 } { 81 }$ when t = 9.

If $f ( x ) = - \frac { 5 } { x + 1 }$ find $f ( - 6 ) , f ( 0 ) , f ( - 1 ) , f ( 4 )$ .

If g ( x ) = 4 x + 3 and f ( x ) = 5 x 2 $-$ 9, find $( g \circ f ) ( 3 )$ .

Specify the domain for the following relation. Please enter your answer in interval notation. {( x , y ) | 9 y $-$ 7 x = 15}

Graph the function. $f ( x ) = - 2 ( x - 1 ) ^ { 2 } - 6$

Graph the function. $f ( x ) = \sqrt { 7 - x }$

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

Identify the graph of the function. f ( x ) = $-$ 3 x 2 $-$ 8 x

Identify the graph of the function. f ( x ) = x 2 $-$ 3 x $-$ 1

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

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

Graph the function. f(x)=−4∣x∣f ( x ) = - 4 | x |f(x)=−4∣x∣

For each of the quadratic functions find its graph. Match each function with the corresponding graph. -

Specify the domain for the function. h(x)=1x2+4x−32h ( x ) = \frac { 1 } { x ^ { 2 } + 4 x - 32 }h(x)=x2+4x−321​

Specify the range for the following relation. Please enter your answer in interval notation. {( x , y ) | 5 x 2 = 8 y 3}

Specify the domain for the function. f(t)=−2x2+3f ( t ) = \frac { - 2 } { x ^ { 2 } + 3 }f(t)=x2+3−2​

Find the constant of variation for the stated condition: y varies directly as x and inversely as z , and y = 20 when x = 170 and z = 34.

The simple interest earned by a certain amount of money varies jointly as the rate of interest and the time (in years) that the money is invested. If the money is invested at 14% for 2 years, $84 is earned. How much is earned if the money is invested at 15% for 4 years? $__________

Find the constant of variation for the stated condition: y varies directly as x , and y = 125 when x = 100. Please enter your answer as a fraction.

For each of the linear functions find its graph. Match each function with the corresponding graph. -

Find the constant of variation for the stated condition: r varies inversely as the cube of t , and r=181r = \frac { 1 } { 81 }r=811​ when t = 9.

If f(x)=−5x+1f ( x ) = - \frac { 5 } { x + 1 }f(x)=−x+15​ find f(−6),f(0),f(−1),f(4)f ( - 6 ) , f ( 0 ) , f ( - 1 ) , f ( 4 )f(−6),f(0),f(−1),f(4) .

If g ( x ) = 4 x + 3 and f ( x ) = 5 x 2 −-− 9, find (g∘f)(3)( g \circ f ) ( 3 )(g∘f)(3) .

Specify the domain for the following relation. Please enter your answer in interval notation. {( x , y ) | 9 y −-− 7 x = 15}

Graph the function. f(x)=−2(x−1)2−6f ( x ) = - 2 ( x - 1 ) ^ { 2 } - 6f(x)=−2(x−1)2−6

Graph the function. f(x)=7−xf ( x ) = \sqrt { 7 - x }f(x)=7−x​

Graph the function. f(x)=1x−1f ( x ) = \frac { 1 } { x - 1 }f(x)=x−11​

Identify the graph of the function. f ( x ) = −-− 3 x 2 −-− 8 x

Identify the graph of the function. f ( x ) = x 2 −-− 3 x −-− 1

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

Graph the function. $f ( x ) = - 4 | x |$

Specify the domain for the function. $h ( x ) = \frac { 1 } { x ^ { 2 } + 4 x - 32 }$

Specify the range for the following relation. Please enter your answer in interval notation. {( x , y ) | 5 x ² = 8 y ³}

Specify the domain for the function. $f ( t ) = \frac { - 2 } { x ^ { 2 } + 3 }$

Find the constant of variation for the stated condition: r varies inversely as the cube of t , and $r = \frac { 1 } { 81 }$ when t = 9.

If $f ( x ) = - \frac { 5 } { x + 1 }$ find $f ( - 6 ) , f ( 0 ) , f ( - 1 ) , f ( 4 )$ .

If g ( x ) = 4 x + 3 and f ( x ) = 5 x 2 $-$ 9, find $( g \circ f ) ( 3 )$ .

Specify the domain for the following relation. Please enter your answer in interval notation. {( x , y ) | 9 y $-$ 7 x = 15}

Graph the function. $f ( x ) = - 2 ( x - 1 ) ^ { 2 } - 6$

Graph the function. $f ( x ) = \sqrt { 7 - x }$

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

Identify the graph of the function. f ( x ) = $-$ 3 x 2 $-$ 8 x

Identify the graph of the function. f ( x ) = x 2 $-$ 3 x $-$ 1