Exam 3: Graphs and Functions

Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such. - $\mathrm { h } ( \mathrm { x } ) = 5$ $Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such. - \mathrm { h } ( \mathrm { x } ) = 5$

(Multiple Choice)

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Question 241

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = 2 - 9 x , g ( x ) = - 5 x ^ { 2 } + 9$ Find $( f + g ) ( x )$ .

(Multiple Choice)

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Question 242

Write an equation for the line described. Write the equation in the form specified. -perpendicular to y = -6, through (1, 3)

(Multiple Choice)

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Question 243

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

(Multiple Choice)

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Question 244

Write all linear equations in slope-intercept form. -A driver wants to gauge the fuel efficiency of her vehicle at speeds of 30 mph and above. She notices that traveling at an average speed of 45 mph results in a rating of 38 mpg, whereas at an Average speed of 55 mph, her car rates 23 mpg. Find a linear equation to model the gas mileage y For an average speed of x mph. Find the slope-intercept form of the equation of the line.

(Multiple Choice)

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Question 245

Evaluate the function. -Find $\left( \frac { 1 } { 2 } \right)$ when $f ( x ) = 3 x ^ { 2 } + 4 x - 1$

(Multiple Choice)

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Question 246

Determine whether the three points are the vertices of a right triangle. -(-9, 9), (2, -2), (4, 0)

(Multiple Choice)

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Question 247

Graph the line described. -through (-10, 6); m = 0

(Multiple Choice)

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Question 248

Give a rule for the piecewise-defined function. Then give the domain and range. -

(Multiple Choice)

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Question 249

Write an equation for the line described. Give your answer in slope-intercept form. - $\mathrm { m } = - \frac { 3 } { 4 }$ , through $( 1 , - 3 )$

(Multiple Choice)

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Question 250

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = x ^ { 2 } + 1 , g ( x ) = 9 x + 5$ Find $( f g ) ( x )$ .

(Multiple Choice)

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Question 251

Provide an appropriate response. -What is the distance from the origin to the point $( m , - n )$ ?

(Multiple Choice)

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Question 252

Compute and simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$ - $f ( x ) = 4 x - 9$

(Multiple Choice)

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Question 253

Find the center-radius form of the equation of the circle. -center $( - 8 , - 10 )$ , radius 8

(Multiple Choice)

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Question 254

Find the specified domain. -Find the domain of $\left( \frac { f } { g } \right) ( x )$ when $f ( x ) = 2 x - 6$ and $g ( x ) = 5 x - 2$

(Multiple Choice)

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Question 255

Provide an appropriate response. -Are the points A(-1, 12), B(2, 9), C(4, 1), and D(7, 4) the vertices of a parallelogram (opposite side equal in length)? of a rhombus (all sides equal in length)?

(Multiple Choice)

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Question 256

Write an equation for the line described. Give your answer in slope-intercept form. - $\mathrm { m } = - 3 , \mathrm {~b} = 9$

(Multiple Choice)

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Question 257

Write an equation for the line described. Give your answer in slope-intercept form. - $m = - 5$ , through $( - 5,6 )$

(Multiple Choice)

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Question 258

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

(Multiple Choice)

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Question 259

An equation that defines y as a function of x is given. Rewrite the equation using function notation f(x). - $x - 2 y = 14$

(Multiple Choice)

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Question 260

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = 2 - 9 x , g ( x ) = - 5 x ^ { 2 } + 9$ Find $( f + g ) ( x )$ .

Write an equation for the line described. Write the equation in the form specified. -perpendicular to y = -6, through (1, 3)

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

Evaluate the function. -Find $\left( \frac { 1 } { 2 } \right)$ when $f ( x ) = 3 x ^ { 2 } + 4 x - 1$

Determine whether the three points are the vertices of a right triangle. -(-9, 9), (2, -2), (4, 0)

Graph the line described. -through (-10, 6); m = 0

Give a rule for the piecewise-defined function. Then give the domain and range. -

Write an equation for the line described. Give your answer in slope-intercept form. - $\mathrm { m } = - \frac { 3 } { 4 }$ , through $( 1 , - 3 )$

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = x ^ { 2 } + 1 , g ( x ) = 9 x + 5$ Find $( f g ) ( x )$ .

Provide an appropriate response. -What is the distance from the origin to the point $( m , - n )$ ?

Compute and simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$ - $f ( x ) = 4 x - 9$

Find the center-radius form of the equation of the circle. -center $( - 8 , - 10 )$ , radius 8

Find the specified domain. -Find the domain of $\left( \frac { f } { g } \right) ( x )$ when $f ( x ) = 2 x - 6$ and $g ( x ) = 5 x - 2$

Provide an appropriate response. -Are the points A(-1, 12), B(2, 9), C(4, 1), and D(7, 4) the vertices of a parallelogram (opposite side equal in length)? of a rhombus (all sides equal in length)?

Write an equation for the line described. Give your answer in slope-intercept form. - $\mathrm { m } = - 3 , \mathrm {~b} = 9$

Write an equation for the line described. Give your answer in slope-intercept form. - $m = - 5$ , through $( - 5,6 )$

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

An equation that defines y as a function of x is given. Rewrite the equation using function notation f(x). - $x - 2 y = 14$

Review of Basic Concepts

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

Filters

Exam 3: Graphs and Functions

Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such. - h(x)=5\mathrm { h } ( \mathrm { x } ) = 5h(x)=5

For the pair of functions, find the indicated sum, difference, product, or quotient. - f(x)=2−9x,g(x)=−5x2+9f ( x ) = 2 - 9 x , g ( x ) = - 5 x ^ { 2 } + 9f(x)=2−9x,g(x)=−5x2+9 Find (f+g)(x)( f + g ) ( x )(f+g)(x) .

Write an equation for the line described. Write the equation in the form specified. -perpendicular to y = -6, through (1, 3)

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

Evaluate the function. -Find (12)\left( \frac { 1 } { 2 } \right)(21​) when f(x)=3x2+4x−1f ( x ) = 3 x ^ { 2 } + 4 x - 1f(x)=3x2+4x−1

Determine whether the three points are the vertices of a right triangle. -(-9, 9), (2, -2), (4, 0)

Graph the line described. -through (-10, 6); m = 0

Give a rule for the piecewise-defined function. Then give the domain and range. -

Write an equation for the line described. Give your answer in slope-intercept form. - m=−34\mathrm { m } = - \frac { 3 } { 4 }m=−43​ , through (1,−3)( 1 , - 3 )(1,−3)

For the pair of functions, find the indicated sum, difference, product, or quotient. - f(x)=x2+1,g(x)=9x+5f ( x ) = x ^ { 2 } + 1 , g ( x ) = 9 x + 5f(x)=x2+1,g(x)=9x+5 Find (fg)(x)( f g ) ( x )(fg)(x) .

Provide an appropriate response. -What is the distance from the origin to the point (m,−n)( m , - n )(m,−n) ?

Compute and simplify the difference quotient f(x+h)−f(x)h,h≠0\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0hf(x+h)−f(x)​,h=0 - f(x)=4x−9f ( x ) = 4 x - 9f(x)=4x−9

Find the center-radius form of the equation of the circle. -center (−8,−10)( - 8 , - 10 )(−8,−10) , radius 8

Find the specified domain. -Find the domain of (fg)(x)\left( \frac { f } { g } \right) ( x )(gf​)(x) when f(x)=2x−6f ( x ) = 2 x - 6f(x)=2x−6 and g(x)=5x−2g ( x ) = 5 x - 2g(x)=5x−2

Provide an appropriate response. -Are the points A(-1, 12), B(2, 9), C(4, 1), and D(7, 4) the vertices of a parallelogram (opposite side equal in length)? of a rhombus (all sides equal in length)?

Write an equation for the line described. Give your answer in slope-intercept form. - m=−3, b=9\mathrm { m } = - 3 , \mathrm {~b} = 9m=−3, b=9

Write an equation for the line described. Give your answer in slope-intercept form. - m=−5m = - 5m=−5 , through (−5,6)( - 5,6 )(−5,6)

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

An equation that defines y as a function of x is given. Rewrite the equation using function notation f(x). - x−2y=14x - 2 y = 14x−2y=14

Review of Basic Concepts

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

Filters

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = 2 - 9 x , g ( x ) = - 5 x ^ { 2 } + 9$ Find $( f + g ) ( x )$ .

Evaluate the function. -Find $\left( \frac { 1 } { 2 } \right)$ when $f ( x ) = 3 x ^ { 2 } + 4 x - 1$

Write an equation for the line described. Give your answer in slope-intercept form. - $\mathrm { m } = - \frac { 3 } { 4 }$ , through $( 1 , - 3 )$

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = x ^ { 2 } + 1 , g ( x ) = 9 x + 5$ Find $( f g ) ( x )$ .

Provide an appropriate response. -What is the distance from the origin to the point $( m , - n )$ ?

Compute and simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$ - $f ( x ) = 4 x - 9$

Find the center-radius form of the equation of the circle. -center $( - 8 , - 10 )$ , radius 8

Find the specified domain. -Find the domain of $\left( \frac { f } { g } \right) ( x )$ when $f ( x ) = 2 x - 6$ and $g ( x ) = 5 x - 2$

Write an equation for the line described. Give your answer in slope-intercept form. - $\mathrm { m } = - 3 , \mathrm {~b} = 9$

Write an equation for the line described. Give your answer in slope-intercept form. - $m = - 5$ , through $( - 5,6 )$

An equation that defines y as a function of x is given. Rewrite the equation using function notation f(x). - $x - 2 y = 14$