Exam 3: Graphs and Functions

Write all linear equations in slope-intercept form. -Suppose that a sales person observes that if an item is priced at $10 per item then 4 items are sold. If 2 items are sold for $12 per item then find a linear equation to model the number y of items sold for x dollars per item. Find The slope-intercept form of the equation of the line.

(Multiple Choice)

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Question 101

Decide whether the relation defines a function. -

(Multiple Choice)

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Question 102

Determine the largest open intervals of the domain over which the function is increasing, decreasing, and constant. -

(Multiple Choice)

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Question 103

Find the specified domain. -Find the domain of $( f - g ) ( x )$ when $f ( x ) = \frac { 2 x } { x - 8 }$ and $g ( x ) = \frac { 4 } { x + 3 }$

(Multiple Choice)

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Question 104

Find the slope and the y-intercept of the line. - $4 x - y = - 3$

(Multiple Choice)

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Question 105

Match the description with the correct symbolic expression. -a line with a negative slope

(Multiple Choice)

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Question 106

Give the domain and range of the relation. -

(Multiple Choice)

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Question 107

Find the requested value. - $f ( x ) = \left\{ \begin{array} { l l } 2 x ^ { 2 } , & \text { if } x \leq - 1 \\2 , & \text { if } - 1 < x < 1 \\2 x + 1 , & \text { if } x \geq 1\end{array} \right.$ $Find the requested value. - f ( x ) = \left\{ \begin{array} { l l } 2 x ^ { 2 } , & \text { if } x \leq - 1 \\ 2 , & \text { if } - 1 < x < 1 \\ 2 x + 1 , & \text { if } x \geq 1 \end{array} \right.$

(Multiple Choice)

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Question 108

Use the graph to solve the problem. -The graph shows the relationship between the area A of a rectangle and the length L, if the width is fixed. Find the area if the length is 4 cm.

(Multiple Choice)

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Question 109

Decide whether the relation defines a function. -

(Multiple Choice)

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Question 110

Write an equation for the line described. Write the equation in the form specified. -parallel to $\mathrm { y } = - 9$ , through $( 5,3 )$

(Multiple Choice)

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Question 111

The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport. -At what time was the temperature its lowest?

(Multiple Choice)

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Question 112

Determine whether the three points are the vertices of a right triangle. - $( 3 , - 5 ) , ( 9 , - 3 ) , ( 15 , - 10 )$

(True/False)

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Question 113

Provide an appropriate response. -What is the distance from the point (a, w) to the point (m, q)?

(Multiple Choice)

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Question 114

Match the equation with the correct graph. - $5 x + 2 y = - 2$

(Multiple Choice)

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Question 115

Use the graphs to find the value of (fg)(1).

(Multiple Choice)

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Question 116

Determine whether $( f \circ g ) ( x ) = x \text { and whether } ( g \circ f ) ( x ) = x \text {. }$ - $f ( x ) = x ^ { 3 } + 8 , g ( x ) = \sqrt [ 3 ] { x - 8 }$

(Multiple Choice)

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Question 117

Give the domain and range of the relation. - $y = \frac { - 9 } { x - 5 }$

(Multiple Choice)

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Question 118

Give the domain and range of the relation. -Find $f ( 3 )$ when $f ( x ) = x ^ { 2 } + 5 x + 1$

(Multiple Choice)

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Question 119

Give the domain and range of the relation. -Find $f \left( \frac { 1 } { 3 } \right)$ when $f ( x ) = - 5 x ^ { 2 } - 6 x - 7$

(Multiple Choice)

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Question 120

Decide whether the relation defines a function. -

Determine the largest open intervals of the domain over which the function is increasing, decreasing, and constant. -

Find the specified domain. -Find the domain of $( f - g ) ( x )$ when $f ( x ) = \frac { 2 x } { x - 8 }$ and $g ( x ) = \frac { 4 } { x + 3 }$

Find the slope and the y-intercept of the line. - $4 x - y = - 3$

Match the description with the correct symbolic expression. -a line with a negative slope

Give the domain and range of the relation. -

Use the graph to solve the problem. -The graph shows the relationship between the area A of a rectangle and the length L, if the width is fixed. Find the area if the length is 4 cm.

Decide whether the relation defines a function. -

Write an equation for the line described. Write the equation in the form specified. -parallel to $\mathrm { y } = - 9$ , through $( 5,3 )$

The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport. -At what time was the temperature its lowest?

Determine whether the three points are the vertices of a right triangle. - $( 3 , - 5 ) , ( 9 , - 3 ) , ( 15 , - 10 )$

Provide an appropriate response. -What is the distance from the point (a, w) to the point (m, q)?

Match the equation with the correct graph. - $5 x + 2 y = - 2$

Use the graphs to find the value of (fg)(1).

Determine whether $( f \circ g ) ( x ) = x \text { and whether } ( g \circ f ) ( x ) = x \text {. }$ - $f ( x ) = x ^ { 3 } + 8 , g ( x ) = \sqrt [ 3 ] { x - 8 }$

Give the domain and range of the relation. - $y = \frac { - 9 } { x - 5 }$

Give the domain and range of the relation. -Find $f ( 3 )$ when $f ( x ) = x ^ { 2 } + 5 x + 1$

Give the domain and range of the relation. -Find $f \left( \frac { 1 } { 3 } \right)$ when $f ( x ) = - 5 x ^ { 2 } - 6 x - 7$

Review of Basic Concepts

Equations and Inequalities

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 3: Graphs and Functions

Decide whether the relation defines a function. -

Determine the largest open intervals of the domain over which the function is increasing, decreasing, and constant. -

Find the specified domain. -Find the domain of (f−g)(x)( f - g ) ( x )(f−g)(x) when f(x)=2xx−8f ( x ) = \frac { 2 x } { x - 8 }f(x)=x−82x​ and g(x)=4x+3g ( x ) = \frac { 4 } { x + 3 }g(x)=x+34​

Find the slope and the y-intercept of the line. - 4x−y=−34 x - y = - 34x−y=−3

Match the description with the correct symbolic expression. -a line with a negative slope

Give the domain and range of the relation. -

Use the graph to solve the problem. -The graph shows the relationship between the area A of a rectangle and the length L, if the width is fixed. Find the area if the length is 4 cm.

Decide whether the relation defines a function. -

Write an equation for the line described. Write the equation in the form specified. -parallel to y=−9\mathrm { y } = - 9y=−9 , through (5,3)( 5,3 )(5,3)

The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport. -At what time was the temperature its lowest?

Determine whether the three points are the vertices of a right triangle. - (3,−5),(9,−3),(15,−10)( 3 , - 5 ) , ( 9 , - 3 ) , ( 15 , - 10 )(3,−5),(9,−3),(15,−10)

Provide an appropriate response. -What is the distance from the point (a, w) to the point (m, q)?

Match the equation with the correct graph. - 5x+2y=−25 x + 2 y = - 25x+2y=−2

Use the graphs to find the value of (fg)(1).

Determine whether (f∘g)(x)=x and whether (g∘f)(x)=x. ( f \circ g ) ( x ) = x \text { and whether } ( g \circ f ) ( x ) = x \text {. }(f∘g)(x)=x and whether (g∘f)(x)=x. - f(x)=x3+8,g(x)=x−83f ( x ) = x ^ { 3 } + 8 , g ( x ) = \sqrt [ 3 ] { x - 8 }f(x)=x3+8,g(x)=3x−8​

Give the domain and range of the relation. - y=−9x−5y = \frac { - 9 } { x - 5 }y=x−5−9​

Give the domain and range of the relation. -Find f(3)f ( 3 )f(3) when f(x)=x2+5x+1f ( x ) = x ^ { 2 } + 5 x + 1f(x)=x2+5x+1

Give the domain and range of the relation. -Find f(13)f \left( \frac { 1 } { 3 } \right)f(31​) when f(x)=−5x2−6x−7f ( x ) = - 5 x ^ { 2 } - 6 x - 7f(x)=−5x2−6x−7

Review of Basic Concepts

Equations and Inequalities

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Find the specified domain. -Find the domain of $( f - g ) ( x )$ when $f ( x ) = \frac { 2 x } { x - 8 }$ and $g ( x ) = \frac { 4 } { x + 3 }$

Find the slope and the y-intercept of the line. - $4 x - y = - 3$

Write an equation for the line described. Write the equation in the form specified. -parallel to $\mathrm { y } = - 9$ , through $( 5,3 )$

Determine whether the three points are the vertices of a right triangle. - $( 3 , - 5 ) , ( 9 , - 3 ) , ( 15 , - 10 )$

Match the equation with the correct graph. - $5 x + 2 y = - 2$

Determine whether $( f \circ g ) ( x ) = x \text { and whether } ( g \circ f ) ( x ) = x \text {. }$ - $f ( x ) = x ^ { 3 } + 8 , g ( x ) = \sqrt [ 3 ] { x - 8 }$

Give the domain and range of the relation. - $y = \frac { - 9 } { x - 5 }$

Give the domain and range of the relation. -Find $f ( 3 )$ when $f ( x ) = x ^ { 2 } + 5 x + 1$

Give the domain and range of the relation. -Find $f \left( \frac { 1 } { 3 } \right)$ when $f ( x ) = - 5 x ^ { 2 } - 6 x - 7$