Exam 1: Functions and Their Graphs

Graph the function and determine the interval(s) for which $f ( x ) \geq 0$ . $f ( x ) = - x ^ { 2 } + 4 x$ $Graph the function and determine the interval(s) for which f ( x ) \geq 0 . f ( x ) = - x ^ { 2 } + 4 x$

(Multiple Choice)

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Question 101

Which equation does not represent y as a function of x?

(Multiple Choice)

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Question 102

Find $f \circ g$ . $f ( x ) = x + 3 \quad g ( x ) = \frac { 4 } { x ^ { 2 } - 9 }$

(Multiple Choice)

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Question 103

Use the graph of $f$ to sketch the graph of the function indicated below.

(Multiple Choice)

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Question 104

Find the slope-intercept form of the line passing through the points. $( - 4 , - 2 ) , ( - 1,7 )$

(Multiple Choice)

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Question 105

Determine an equation that may represented by the graph shown below.

(Multiple Choice)

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Question 106

Find the slope-intercept form of the line passing through the points. $( - 1 , - 6 ) , ( 0 , - 2 )$

(Multiple Choice)

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Question 107

If $f$ is an even function, determine if $g$ is even, odd, or neither. $g ( x ) = f ( - x ) + 1$

(Multiple Choice)

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Question 108

Find the value(s) of $x$ for which $f ( x ) = g ( x )$ . $f ( x ) = x ^ { 2 } - 7 x + 3 \quadg ( x ) = - 3 x + 8$

(Multiple Choice)

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Question 109

Find $f \circ g$ . $f ( x ) = 3 x - 2 \quad g ( x ) = x - 5$

(Multiple Choice)

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Question 110

Find all real values of $x$ such that $f ( x ) = 0$ . $f ( x ) = 49 x ^ { 2 } - 64$

(Multiple Choice)

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Question 111

Compare the graph of the following function with the graph of $f ( x ) = | x |$ . $y = \left| \frac { 1 } { 9 } x \right|$

(Multiple Choice)

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Question 112

Use function notation to write $g$ in terms of $f ( x ) = x ^ { 3 }$ . $g ( x ) = - \frac { 1 } { 5 } ( x + 4 ) ^ { 3 }$

(Multiple Choice)

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Question 113

Determine an equation that may represented by the graph shown below.

(Multiple Choice)

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Question 114

Restrict the domain of the following function $f$ so that the function is one-to-one and has an inverse function. $f ( x ) = - | x - 4 | + 2$

(Multiple Choice)

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Question 115

Use the graph of $f$ to sketch the graph of the function indicated below.

(Multiple Choice)

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Question 116

Determine an equation that may represented by the graph shown below.

(Multiple Choice)

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Question 117

If $f$ is an even function, determine if $g$ is even, odd, or neither. $g ( x ) = f ( x + 4 )$

(Multiple Choice)

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Question 118

Graph the function and determine the interval(s) for which $f ( x ) \geq 0$ . $f ( x ) = - x ^ { 2 } + 4 x$ $Graph the function and determine the interval(s) for which f ( x ) \geq 0 . f ( x ) = - x ^ { 2 } + 4 x$

Which equation does not represent y as a function of x?

Find $f \circ g$ . $f ( x ) = x + 3 \quad g ( x ) = \frac { 4 } { x ^ { 2 } - 9 }$

Use the graph of $f$ to sketch the graph of the function indicated below.

Find the slope-intercept form of the line passing through the points. $( - 4 , - 2 ) , ( - 1,7 )$

Determine an equation that may represented by the graph shown below.

Find the slope-intercept form of the line passing through the points. $( - 1 , - 6 ) , ( 0 , - 2 )$

If $f$ is an even function, determine if $g$ is even, odd, or neither. $g ( x ) = f ( - x ) + 1$

Find the value(s) of $x$ for which $f ( x ) = g ( x )$ . $f ( x ) = x ^ { 2 } - 7 x + 3 \quadg ( x ) = - 3 x + 8$

Find $f \circ g$ . $f ( x ) = 3 x - 2 \quad g ( x ) = x - 5$

Find all real values of $x$ such that $f ( x ) = 0$ . $f ( x ) = 49 x ^ { 2 } - 64$

Compare the graph of the following function with the graph of $f ( x ) = | x |$ . $y = \left| \frac { 1 } { 9 } x \right|$

Use function notation to write $g$ in terms of $f ( x ) = x ^ { 3 }$ . $g ( x ) = - \frac { 1 } { 5 } ( x + 4 ) ^ { 3 }$

Determine an equation that may represented by the graph shown below.

Restrict the domain of the following function $f$ so that the function is one-to-one and has an inverse function. $f ( x ) = - | x - 4 | + 2$

Use the graph of $f$ to sketch the graph of the function indicated below.

Determine an equation that may represented by the graph shown below.

If $f$ is an even function, determine if $g$ is even, odd, or neither. $g ( x ) = f ( x + 4 )$

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Limits and an Introduction to Calculus

Review of Graphs, Equations, and Inequalities

Filters

Exam 1: Functions and Their Graphs

Graph the function and determine the interval(s) for which f(x)≥0f ( x ) \geq 0f(x)≥0 . f(x)=−x2+4xf ( x ) = - x ^ { 2 } + 4 xf(x)=−x2+4x

Which equation does not represent y as a function of x?

Find f∘gf \circ gf∘g . f(x)=x+3g(x)=4x2−9f ( x ) = x + 3 \quad g ( x ) = \frac { 4 } { x ^ { 2 } - 9 }f(x)=x+3g(x)=x2−94​

Use the graph of fff to sketch the graph of the function indicated below.

Find the slope-intercept form of the line passing through the points. (−4,−2),(−1,7)( - 4 , - 2 ) , ( - 1,7 )(−4,−2),(−1,7)

Determine an equation that may represented by the graph shown below.

Find the slope-intercept form of the line passing through the points. (−1,−6),(0,−2)( - 1 , - 6 ) , ( 0 , - 2 )(−1,−6),(0,−2)

If fff is an even function, determine if ggg is even, odd, or neither. g(x)=f(−x)+1g ( x ) = f ( - x ) + 1g(x)=f(−x)+1

Find the value(s) of xxx for which f(x)=g(x)f ( x ) = g ( x )f(x)=g(x) . f(x)=x2−7x+3\quadg(x)=−3x+8f ( x ) = x ^ { 2 } - 7 x + 3 \quadg ( x ) = - 3 x + 8f(x)=x2−7x+3\quadg(x)=−3x+8

Find f∘gf \circ gf∘g . f(x)=3x−2g(x)=x−5f ( x ) = 3 x - 2 \quad g ( x ) = x - 5f(x)=3x−2g(x)=x−5

Find all real values of xxx such that f(x)=0f ( x ) = 0f(x)=0 . f(x)=49x2−64f ( x ) = 49 x ^ { 2 } - 64f(x)=49x2−64

Compare the graph of the following function with the graph of f(x)=∣x∣f ( x ) = | x |f(x)=∣x∣ . y=∣19x∣y = \left| \frac { 1 } { 9 } x \right|y=​91​x​

Use function notation to write ggg in terms of f(x)=x3f ( x ) = x ^ { 3 }f(x)=x3 . g(x)=−15(x+4)3g ( x ) = - \frac { 1 } { 5 } ( x + 4 ) ^ { 3 }g(x)=−51​(x+4)3

Determine an equation that may represented by the graph shown below.

Restrict the domain of the following function fff so that the function is one-to-one and has an inverse function. f(x)=−∣x−4∣+2f ( x ) = - | x - 4 | + 2f(x)=−∣x−4∣+2

Use the graph of fff to sketch the graph of the function indicated below.

Determine an equation that may represented by the graph shown below.

If fff is an even function, determine if ggg is even, odd, or neither. g(x)=f(x+4)g ( x ) = f ( x + 4 )g(x)=f(x+4)

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Limits and an Introduction to Calculus

Review of Graphs, Equations, and Inequalities

Filters

Graph the function and determine the interval(s) for which $f ( x ) \geq 0$ . $f ( x ) = - x ^ { 2 } + 4 x$ $Graph the function and determine the interval(s) for which f ( x ) \geq 0 . f ( x ) = - x ^ { 2 } + 4 x$

Find $f \circ g$ . $f ( x ) = x + 3 \quad g ( x ) = \frac { 4 } { x ^ { 2 } - 9 }$

Use the graph of $f$ to sketch the graph of the function indicated below.

Find the slope-intercept form of the line passing through the points. $( - 4 , - 2 ) , ( - 1,7 )$

Find the slope-intercept form of the line passing through the points. $( - 1 , - 6 ) , ( 0 , - 2 )$

If $f$ is an even function, determine if $g$ is even, odd, or neither. $g ( x ) = f ( - x ) + 1$

Find the value(s) of $x$ for which $f ( x ) = g ( x )$ . $f ( x ) = x ^ { 2 } - 7 x + 3 \quadg ( x ) = - 3 x + 8$

Find $f \circ g$ . $f ( x ) = 3 x - 2 \quad g ( x ) = x - 5$

Find all real values of $x$ such that $f ( x ) = 0$ . $f ( x ) = 49 x ^ { 2 } - 64$

Compare the graph of the following function with the graph of $f ( x ) = | x |$ . $y = \left| \frac { 1 } { 9 } x \right|$

Use function notation to write $g$ in terms of $f ( x ) = x ^ { 3 }$ . $g ( x ) = - \frac { 1 } { 5 } ( x + 4 ) ^ { 3 }$

Restrict the domain of the following function $f$ so that the function is one-to-one and has an inverse function. $f ( x ) = - | x - 4 | + 2$

Use the graph of $f$ to sketch the graph of the function indicated below.

If $f$ is an even function, determine if $g$ is even, odd, or neither. $g ( x ) = f ( x + 4 )$