Exam 2: Graphs and Functions

Solve the problem. -The locations of three receiving stations and the distances to the epicenter of an earthquake are contained in the following three equations: $( x + 2 ) ^ { 2 } + ( y - 8 ) ^ { 2 } = 16 , ( x + 7 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 25$ , $( x - 4 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 100$ . Determine the location of the epicenter.

(Multiple Choice)

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Question 101

Consider the function h as defined. Find functions f and g so that (f ∘ g)(x) = h(x). - $h ( x ) = \frac { 10 } { x ^ { 2 } } + 7$

(Multiple Choice)

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Question 102

Graph the function. -

(Multiple Choice)

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Question 103

Solve the problem. -In Country X, the average hourly wage in dollars from 1960 to 2010 can be modeled by $f ( x ) = \left\{ \begin{array} { l l } 0.078 ( x - 1960 ) + 0.32 & \text { if } 1960 \leq x < 1995 \\0.184 ( x - 1995 ) + 3.04 & \text { if } 1995 \leq x \leq 2010\end{array} \right.$ Use $f$ to estimate the average hourly wages in 1965,1985 , and $2005 .$

(Multiple Choice)

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Question 104

Determine whether the equation has a graph that is symmetric with respect to the y -axis, the x-axis, the origin, or none of these. -y = (x - 6)(x + 3)

(Multiple Choice)

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Question 105

Consider the function h as defined. Find functions f and g so that (f ∘ g)(x) = h(x). - $h ( x ) = \frac { 1 } { x ^ { 2 } - 7 }$

(Multiple Choice)

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Question 106

Graph the point symmetric to the given point. -Plot the point (-2, -1), then plot the point that is symmetric to (-2, -1) with respect to the x-axis.

(Multiple Choice)

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Question 107

Describe the transformations and give the equation for the graph. -

(Multiple Choice)

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Question 108

Decide whether the relation defines a function. - $x = y ^ { 2 }$

(Multiple Choice)

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Question 109

Match the equation with the correct graph. - $y = - \frac { 1 } { 4 } x + 1$

(Multiple Choice)

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Question 110

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = 6 - 4 x , g ( x ) = - 9 x ^ { 2 } + 4$ Find $( f + g ) ( x )$ .

(Multiple Choice)

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Question 111

Use a graphing calculator to solve the linear equation. - $4 ( 2 z - 2 ) = 7 ( z + 4 )$

(Multiple Choice)

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Question 112

Graph the equation by plotting points. - $y=-x^{2}+1$ $Graph the equation by plotting points. - y=-x^{2}+1$

(Multiple Choice)

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Question 113

Graph the function. - $f(x)=7 x^{2}$ $Graph the function. - f(x)=7 x^{2}$

(Multiple Choice)

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Question 114

Write an equation for the line described. Give your answer in standard form. -through $( 1,5 )$ , undefined slope

(Multiple Choice)

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Question 115

Give the domain and range of the relation. - $y = \frac { - 8 } { x - 4 }$

(Multiple Choice)

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Question 116

Give the domain and range of the relation. -

(Multiple Choice)

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Question 117

Graph the line described. - $\text { through }(0,4) ; \mathrm{m}=-\frac{1}{4}$ $Graph the line described. - \text { through }(0,4) ; \mathrm{m}=-\frac{1}{4}$

(Multiple Choice)

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Question 118

The graph of a linear function f is shown. Write the equation that defines f. Write the equation in slope -intercept form. -

(Multiple Choice)

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Question 119

Find the slope of the line and sketch the graph. - $2 x-3 y=-8$

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Question 120

Consider the function h as defined. Find functions f and g so that (f ∘ g)(x) = h(x). - $h ( x ) = \frac { 10 } { x ^ { 2 } } + 7$

Graph the function. -

Determine whether the equation has a graph that is symmetric with respect to the y -axis, the x-axis, the origin, or none of these. -y = (x - 6)(x + 3)

Consider the function h as defined. Find functions f and g so that (f ∘ g)(x) = h(x). - $h ( x ) = \frac { 1 } { x ^ { 2 } - 7 }$

Graph the point symmetric to the given point. -Plot the point (-2, -1), then plot the point that is symmetric to (-2, -1) with respect to the x-axis.

Describe the transformations and give the equation for the graph. -

Decide whether the relation defines a function. - $x = y ^ { 2 }$

Match the equation with the correct graph. - $y = - \frac { 1 } { 4 } x + 1$

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = 6 - 4 x , g ( x ) = - 9 x ^ { 2 } + 4$ Find $( f + g ) ( x )$ .

Use a graphing calculator to solve the linear equation. - $4 ( 2 z - 2 ) = 7 ( z + 4 )$

Graph the equation by plotting points. - $y=-x^{2}+1$ $Graph the equation by plotting points. - y=-x^{2}+1$

Graph the function. - $f(x)=7 x^{2}$ $Graph the function. - f(x)=7 x^{2}$

Write an equation for the line described. Give your answer in standard form. -through $( 1,5 )$ , undefined slope

Give the domain and range of the relation. - $y = \frac { - 8 } { x - 4 }$

Give the domain and range of the relation. -

Graph the line described. - $\text { through }(0,4) ; \mathrm{m}=-\frac{1}{4}$ $Graph the line described. - \text { through }(0,4) ; \mathrm{m}=-\frac{1}{4}$

The graph of a linear function f is shown. Write the equation that defines f. Write the equation in slope -intercept form. -

Find the slope of the line and sketch the graph. - $2 x-3 y=-8$

Equations and Inequalities

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Exam 2: Graphs and Functions

Consider the function h as defined. Find functions f and g so that (f ∘ g)(x) = h(x). - h(x)=10x2+7h ( x ) = \frac { 10 } { x ^ { 2 } } + 7h(x)=x210​+7

Graph the function. -

Determine whether the equation has a graph that is symmetric with respect to the y -axis, the x-axis, the origin, or none of these. -y = (x - 6)(x + 3)

Consider the function h as defined. Find functions f and g so that (f ∘ g)(x) = h(x). - h(x)=1x2−7h ( x ) = \frac { 1 } { x ^ { 2 } - 7 }h(x)=x2−71​

Graph the point symmetric to the given point. -Plot the point (-2, -1), then plot the point that is symmetric to (-2, -1) with respect to the x-axis.

Describe the transformations and give the equation for the graph. -

Decide whether the relation defines a function. - x=y2x = y ^ { 2 }x=y2

Match the equation with the correct graph. - y=−14x+1y = - \frac { 1 } { 4 } x + 1y=−41​x+1

For the pair of functions, find the indicated sum, difference, product, or quotient. - f(x)=6−4x,g(x)=−9x2+4f ( x ) = 6 - 4 x , g ( x ) = - 9 x ^ { 2 } + 4f(x)=6−4x,g(x)=−9x2+4 Find (f+g)(x)( f + g ) ( x )(f+g)(x) .

Use a graphing calculator to solve the linear equation. - 4(2z−2)=7(z+4)4 ( 2 z - 2 ) = 7 ( z + 4 )4(2z−2)=7(z+4)

Graph the equation by plotting points. - y=−x2+1y=-x^{2}+1y=−x2+1

Graph the function. - f(x)=7x2f(x)=7 x^{2}f(x)=7x2

Write an equation for the line described. Give your answer in standard form. -through (1,5)( 1,5 )(1,5) , undefined slope

Give the domain and range of the relation. - y=−8x−4y = \frac { - 8 } { x - 4 }y=x−4−8​

Give the domain and range of the relation. -

Graph the line described. - through (0,4);m=−14\text { through }(0,4) ; \mathrm{m}=-\frac{1}{4} through (0,4);m=−41​

The graph of a linear function f is shown. Write the equation that defines f. Write the equation in slope -intercept form. -

Find the slope of the line and sketch the graph. - 2x−3y=−82 x-3 y=-82x−3y=−8

Equations and Inequalities

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Consider the function h as defined. Find functions f and g so that (f ∘ g)(x) = h(x). - $h ( x ) = \frac { 10 } { x ^ { 2 } } + 7$

Consider the function h as defined. Find functions f and g so that (f ∘ g)(x) = h(x). - $h ( x ) = \frac { 1 } { x ^ { 2 } - 7 }$

Decide whether the relation defines a function. - $x = y ^ { 2 }$

Match the equation with the correct graph. - $y = - \frac { 1 } { 4 } x + 1$

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = 6 - 4 x , g ( x ) = - 9 x ^ { 2 } + 4$ Find $( f + g ) ( x )$ .

Use a graphing calculator to solve the linear equation. - $4 ( 2 z - 2 ) = 7 ( z + 4 )$

Graph the equation by plotting points. - $y=-x^{2}+1$ $Graph the equation by plotting points. - y=-x^{2}+1$

Graph the function. - $f(x)=7 x^{2}$ $Graph the function. - f(x)=7 x^{2}$

Write an equation for the line described. Give your answer in standard form. -through $( 1,5 )$ , undefined slope

Give the domain and range of the relation. - $y = \frac { - 8 } { x - 4 }$

Graph the line described. - $\text { through }(0,4) ; \mathrm{m}=-\frac{1}{4}$ $Graph the line described. - \text { through }(0,4) ; \mathrm{m}=-\frac{1}{4}$

Find the slope of the line and sketch the graph. - $2 x-3 y=-8$