Exam 13: Functions

The intensity of illumination ( B ) received from a source of light is inversely proportional to the square of the distance ( d ) from the source. Translate the statement of variation into an equation and use k as the constant of variation.

(Short Answer)

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Question 41

If g ( x ) = 8 x + 4 and f ( x ) = 5 x 2 $-$ 9, find $( f \circ g ) ( 4 ) \text { and } ( g \circ f ) ( 4 )$ . Match each expression with the corresponding answer. - $6,471$

(Multiple Choice)

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Question 42

The cost for burning a 75-watt bulb is given by the function c ( h ) = 0.0045 h , where h represents the number of hours that the bulb burns. How much does it cost to burn a 75-watt bulb for 3 hours per night for a 31-day month? Express your answer to the nearest cent.

(Multiple Choice)

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Question 43

Find the vertex of $f ( x ) = 2 x ^ { 2 } - 3 x - 4$ .

(Multiple Choice)

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Question 44

Suppose that the equation p ( x ) = $-$ 2 x 2 + 280 x $-$ 2,540, where x represents the number of items sold, describes the profit function for a certain business. How many items should be sold to maximize the profit? __________ items

(Short Answer)

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Question 45

If $f ( x ) = \frac { 9 } { x } \text { and } g ( x ) = \frac { 9 } { x - 2 } \text {, }$ find $( f \circ g ) ( 4 )$ .

(Multiple Choice)

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Question 46

If f ( x ) = |9 x $-$ 5| and g ( x ) = x 3 , find $( f \circ g ) ( 1 ) \text { and } ( g \circ f ) ( 1 )$ . Match each expression with the corresponding answer. - $4$

(Multiple Choice)

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Question 47

The time required for a car to travel a certain distance varies inversely as the rate at which it travels. If it takes 2 hours at 60 miles per hour to travel the distance, how long will it take at 20 miles per hour? __________ hours

(Short Answer)

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Question 48

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

(Multiple Choice)

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Question 49

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 $y = 8 \frac { 1 } { 6 }$ when x = 42 and z = 36.

(Multiple Choice)

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Question 50

Translations and reflections are called static transformations because the basic shape of the curve being transformed is not changed.

(True/False)

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Question 51

Determine $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = \frac { 1 } { x } \text { and } g ( x ) = \frac { 1 } { x - 7 }$

(Multiple Choice)

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Question 52

Determine $( g \circ f ) ( x )$ for the pair of functions f ( x ) = 9 x and g ( x ) = 3 x $-$ 4.

(Multiple Choice)

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Question 53

Suppose that the equation p ( x ) = $-$ 5 x 2 + 600 x $-$ 4,705, where x represents the number of items sold, describes the profit function for a certain business. How many items should be sold to maximize the profit?

(Multiple Choice)

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Question 54

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

(Multiple Choice)

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Question 55

The distance that a freely falling body falls varies directly as the square of the time it falls. If a body falls 612 feet in 6 seconds, how far will it fall in 9 seconds? __________ feet

(Short Answer)

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Question 56

Identify the graph of the function. f ( x ) = 3 x $-$ 5

(Multiple Choice)

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Question 57

Three hundred meters of fencing is available to enclose a rectangular playground. What should be the dimensions of the playground to maximize the area?

(Short Answer)

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Question 58

If f ( x ) = 3 x $-$ 2 and g ( x ) = $-$ 6 x + 3, find $( f \circ g ) ( 8 ) \text { and } ( g \circ f ) ( 8 )$ . Match each expression with the corresponding answer. - $- 137$

(Multiple Choice)

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Question 59

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 10 inches long. Express your answer to the nearest tenth of a second. __________ seconds

(Short Answer)

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Question 60

The intensity of illumination ( B ) received from a source of light is inversely proportional to the square of the distance ( d ) from the source. Translate the statement of variation into an equation and use k as the constant of variation.

If g ( x ) = 8 x + 4 and f ( x ) = 5 x 2 $-$ 9, find $( f \circ g ) ( 4 ) \text { and } ( g \circ f ) ( 4 )$ . Match each expression with the corresponding answer. - $6,471$

The cost for burning a 75-watt bulb is given by the function c ( h ) = 0.0045 h , where h represents the number of hours that the bulb burns. How much does it cost to burn a 75-watt bulb for 3 hours per night for a 31-day month? Express your answer to the nearest cent.

Find the vertex of $f ( x ) = 2 x ^ { 2 } - 3 x - 4$ .

Suppose that the equation p ( x ) = $-$ 2 x 2 + 280 x $-$ 2,540, where x represents the number of items sold, describes the profit function for a certain business. How many items should be sold to maximize the profit? __________ items

If $f ( x ) = \frac { 9 } { x } \text { and } g ( x ) = \frac { 9 } { x - 2 } \text {, }$ find $( f \circ g ) ( 4 )$ .

If f ( x ) = |9 x $-$ 5| and g ( x ) = x 3 , find $( f \circ g ) ( 1 ) \text { and } ( g \circ f ) ( 1 )$ . Match each expression with the corresponding answer. - $4$

The time required for a car to travel a certain distance varies inversely as the rate at which it travels. If it takes 2 hours at 60 miles per hour to travel the distance, how long will it take at 20 miles per hour? __________ hours

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: y is directly proportional to the square of x and inversely proportional to the cube of z , and $y = 8 \frac { 1 } { 6 }$ when x = 42 and z = 36.

Translations and reflections are called static transformations because the basic shape of the curve being transformed is not changed.

Determine $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = \frac { 1 } { x } \text { and } g ( x ) = \frac { 1 } { x - 7 }$

Determine $( g \circ f ) ( x )$ for the pair of functions f ( x ) = 9 x and g ( x ) = 3 x $-$ 4.

Suppose that the equation p ( x ) = $-$ 5 x 2 + 600 x $-$ 4,705, where x represents the number of items sold, describes the profit function for a certain business. How many items should be sold to maximize the profit?

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

The distance that a freely falling body falls varies directly as the square of the time it falls. If a body falls 612 feet in 6 seconds, how far will it fall in 9 seconds? __________ feet

Identify the graph of the function. f ( x ) = 3 x $-$ 5

Three hundred meters of fencing is available to enclose a rectangular playground. What should be the dimensions of the playground to maximize the area?

If f ( x ) = 3 x $-$ 2 and g ( x ) = $-$ 6 x + 3, find $( f \circ g ) ( 8 ) \text { and } ( g \circ f ) ( 8 )$ . Match each expression with the corresponding answer. - $- 137$

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 intensity of illumination ( B ) received from a source of light is inversely proportional to the square of the distance ( d ) from the source. Translate the statement of variation into an equation and use k as the constant of variation.

If g ( x ) = 8 x + 4 and f ( x ) = 5 x 2 −-− 9, find (f∘g)(4) and (g∘f)(4)( f \circ g ) ( 4 ) \text { and } ( g \circ f ) ( 4 )(f∘g)(4) and (g∘f)(4) . Match each expression with the corresponding answer. - 6,4716,4716,471

The cost for burning a 75-watt bulb is given by the function c ( h ) = 0.0045 h , where h represents the number of hours that the bulb burns. How much does it cost to burn a 75-watt bulb for 3 hours per night for a 31-day month? Express your answer to the nearest cent.

Find the vertex of f(x)=2x2−3x−4f ( x ) = 2 x ^ { 2 } - 3 x - 4f(x)=2x2−3x−4 .

Suppose that the equation p ( x ) = −-− 2 x 2 + 280 x −-− 2,540, where x represents the number of items sold, describes the profit function for a certain business. How many items should be sold to maximize the profit? __________ items

If f(x)=9x and g(x)=9x−2, f ( x ) = \frac { 9 } { x } \text { and } g ( x ) = \frac { 9 } { x - 2 } \text {, }f(x)=x9​ and g(x)=x−29​, find (f∘g)(4)( f \circ g ) ( 4 )(f∘g)(4) .

If f ( x ) = |9 x −-− 5| and g ( x ) = x 3 , find (f∘g)(1) and (g∘f)(1)( f \circ g ) ( 1 ) \text { and } ( g \circ f ) ( 1 )(f∘g)(1) and (g∘f)(1) . Match each expression with the corresponding answer. - 444

The time required for a car to travel a certain distance varies inversely as the rate at which it travels. If it takes 2 hours at 60 miles per hour to travel the distance, how long will it take at 20 miles per hour? __________ hours

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: y is directly proportional to the square of x and inversely proportional to the cube of z , and y=816y = 8 \frac { 1 } { 6 }y=861​ when x = 42 and z = 36.

Translations and reflections are called static transformations because the basic shape of the curve being transformed is not changed.

Determine (g∘f)(x)( g \circ f ) ( x )(g∘f)(x) for the pair of functions f(x)=1x and g(x)=1x−7f ( x ) = \frac { 1 } { x } \text { and } g ( x ) = \frac { 1 } { x - 7 }f(x)=x1​ and g(x)=x−71​

Determine (g∘f)(x)( g \circ f ) ( x )(g∘f)(x) for the pair of functions f ( x ) = 9 x and g ( x ) = 3 x −-− 4.

Suppose that the equation p ( x ) = −-− 5 x 2 + 600 x −-− 4,705, where x represents the number of items sold, describes the profit function for a certain business. How many items should be sold to maximize the profit?

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

The distance that a freely falling body falls varies directly as the square of the time it falls. If a body falls 612 feet in 6 seconds, how far will it fall in 9 seconds? __________ feet

Identify the graph of the function. f ( x ) = 3 x −-− 5

Three hundred meters of fencing is available to enclose a rectangular playground. What should be the dimensions of the playground to maximize the area?

If f ( x ) = 3 x −-− 2 and g ( x ) = −-− 6 x + 3, find (f∘g)(8) and (g∘f)(8)( f \circ g ) ( 8 ) \text { and } ( g \circ f ) ( 8 )(f∘g)(8) and (g∘f)(8) . Match each expression with the corresponding answer. - −137- 137−137

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 g ( x ) = 8 x + 4 and f ( x ) = 5 x 2 $-$ 9, find $( f \circ g ) ( 4 ) \text { and } ( g \circ f ) ( 4 )$ . Match each expression with the corresponding answer. - $6,471$

Find the vertex of $f ( x ) = 2 x ^ { 2 } - 3 x - 4$ .

Suppose that the equation p ( x ) = $-$ 2 x 2 + 280 x $-$ 2,540, where x represents the number of items sold, describes the profit function for a certain business. How many items should be sold to maximize the profit? __________ items

If $f ( x ) = \frac { 9 } { x } \text { and } g ( x ) = \frac { 9 } { x - 2 } \text {, }$ find $( f \circ g ) ( 4 )$ .

If f ( x ) = |9 x $-$ 5| and g ( x ) = x 3 , find $( f \circ g ) ( 1 ) \text { and } ( g \circ f ) ( 1 )$ . Match each expression with the corresponding answer. - $4$

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 $y = 8 \frac { 1 } { 6 }$ when x = 42 and z = 36.

Determine $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = \frac { 1 } { x } \text { and } g ( x ) = \frac { 1 } { x - 7 }$

Determine $( g \circ f ) ( x )$ for the pair of functions f ( x ) = 9 x and g ( x ) = 3 x $-$ 4.

Suppose that the equation p ( x ) = $-$ 5 x 2 + 600 x $-$ 4,705, where x represents the number of items sold, describes the profit function for a certain business. How many items should be sold to maximize the profit?

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

Identify the graph of the function. f ( x ) = 3 x $-$ 5

If f ( x ) = 3 x $-$ 2 and g ( x ) = $-$ 6 x + 3, find $( f \circ g ) ( 8 ) \text { and } ( g \circ f ) ( 8 )$ . Match each expression with the corresponding answer. - $- 137$