Exam 2: Functions and Relations

Solve the problem. -The graph shows the number of organ transplants $y$ in a certain country for the years 2005 to 2010 where $x$ represents the number of years since 2005 . The linear model $y = 17.0 x + 93$ was created using the points $( 1,110 )$ and $( 4,161 )$ . a. Interpret the meaning of the slope in the context of this problem. b. Interpret the meaning of the $y$ -intercept in the context of this problem.

(Multiple Choice)

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Question 161

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The graph of y = f (3x) is the graph of y = f (x) with a (choose one: vertical stretch, vertical shrink, horizontal stretch, horizontal shrink).

(Short Answer)

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Question 162

Evaluate the function for the indicated value. -Evaluate $f ( - 1 )$ $f ( x ) = \left\{ \begin{array} { c c } 9 & x \leq - 1 \\| x + 1 | & - 1 < x \leq 5 \\- 5 & x > 5\end{array} \right.$

(Multiple Choice)

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Question 163

Evaluate the function for the given value of x. - $f ( x ) = x ^ { 3 } + 6 x , ( f \circ f ) ( 3 ) = \text { ? }$

(Multiple Choice)

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Question 164

Choose the one alternative that best completes the statement or answers the question. Graph the equation and identify the x- and y-intercepts. - $3 x = - 5 y$

(Multiple Choice)

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Question 165

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The graph of a constant function defined by f(x) = b is a (horizontal/vertical) line.

(Short Answer)

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Question 166

Solve the problem. -Find the shortest distance from the origin to a point on the circle defined by $x ^ { 2 } + y ^ { 2 } - 14 x - 18 y + 121 = 0 \text {. }$

(Multiple Choice)

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Question 167

Write the equation in slope-intercept form. Then, graph the line using the slope and y-intercept. - $-3 x+5 y=-15$

(Multiple Choice)

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Question 168

The slope of a line is given. a. Determine the slope of a line parallel to the given line, if possible. b. Determine the slope of a line perpendicular to the given line, if possible. - $m = \frac { 8 } { 5 }$

(Multiple Choice)

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Question 169

Write the given equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Identify the center and radius. - $x ^ { 2 } + y ^ { 2 } - 6 x + 6 y - 82 = 0$

(Multiple Choice)

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Question 170

Write an equation of the line satisfying the given conditions. -The line passes through (42, 17) and is parallel to y = 6.

(Multiple Choice)

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Question 171

Write an equation of the line satisfying the given conditions. Write the answer in standard form with no fractional coefficients. -Passes through $( 4,4 )$ and is perpendicular to the line defined by $- 5 x + 4 y = - 6$

(Multiple Choice)

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Question 172

Use translations to graph the given function. - $f ( x ) = | x + 1 |$

(Multiple Choice)

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Question 173

Determine the center and radius of the circle. - $( x - 4 ) ^ { 2 } + ( y - 8 ) ^ { 2 } = 9$

(Multiple Choice)

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Question 174

Determine the domain and range of the function. -

(Multiple Choice)

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Question 175

Find an equation of the circle with the given characteristics. -Center $( 8 , - 7 )$ and radius 3

(Multiple Choice)

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Question 176

Solve the problem. -A certain medicine is administered to animals based on the weight. The recommended dose is 4 mg per lb of the animal's weight. Construct a linear function and use it to determine what size animal Would require a 1,300-mg dose of the medicine.

(Multiple Choice)

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Question 177

In a rectangular coordinate system, the point where the x- and y-axes meet is called the________

(Short Answer)

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Question 178

Write a function based on the given parent function and the transformations in the given order. -Parent function $y = \frac { 1 } { x }$ 1. Stretch vertically by a factor of 6. 2. Reflect across the x-axis. 3) Shift downward 9 units.

(Multiple Choice)

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Question 179

Write the domain in interval notation. - $a ( x ) = \sqrt { 8 - x }$

(Multiple Choice)

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Question 180

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The graph of y = f (3x) is the graph of y = f (x) with a (choose one: vertical stretch, vertical shrink, horizontal stretch, horizontal shrink).

Evaluate the function for the indicated value. -Evaluate $f ( - 1 )$ $f ( x ) = \left\{ \begin{array} { c c } 9 & x \leq - 1 \\| x + 1 | & - 1 < x \leq 5 \\- 5 & x > 5\end{array} \right.$

Evaluate the function for the given value of x. - $f ( x ) = x ^ { 3 } + 6 x , ( f \circ f ) ( 3 ) = \text { ? }$

Choose the one alternative that best completes the statement or answers the question. Graph the equation and identify the x- and y-intercepts. - $3 x = - 5 y$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The graph of a constant function defined by f(x) = b is a (horizontal/vertical) line.

Solve the problem. -Find the shortest distance from the origin to a point on the circle defined by $x ^ { 2 } + y ^ { 2 } - 14 x - 18 y + 121 = 0 \text {. }$

Write the equation in slope-intercept form. Then, graph the line using the slope and y-intercept. - $-3 x+5 y=-15$

The slope of a line is given. a. Determine the slope of a line parallel to the given line, if possible. b. Determine the slope of a line perpendicular to the given line, if possible. - $m = \frac { 8 } { 5 }$

Write the given equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Identify the center and radius. - $x ^ { 2 } + y ^ { 2 } - 6 x + 6 y - 82 = 0$

Write an equation of the line satisfying the given conditions. -The line passes through (42, 17) and is parallel to y = 6.

Write an equation of the line satisfying the given conditions. Write the answer in standard form with no fractional coefficients. -Passes through $( 4,4 )$ and is perpendicular to the line defined by $- 5 x + 4 y = - 6$

Use translations to graph the given function. - $f ( x ) = | x + 1 |$

Determine the center and radius of the circle. - $( x - 4 ) ^ { 2 } + ( y - 8 ) ^ { 2 } = 9$

Determine the domain and range of the function. -

Find an equation of the circle with the given characteristics. -Center $( 8 , - 7 )$ and radius 3

Solve the problem. -A certain medicine is administered to animals based on the weight. The recommended dose is 4 mg per lb of the animal's weight. Construct a linear function and use it to determine what size animal Would require a 1,300-mg dose of the medicine.

In a rectangular coordinate system, the point where the x- and y-axes meet is called the________

Write a function based on the given parent function and the transformations in the given order. -Parent function $y = \frac { 1 } { x }$ 1. Stretch vertically by a factor of 6. 2. Reflect across the x-axis. 3) Shift downward 9 units.

Write the domain in interval notation. - $a ( x ) = \sqrt { 8 - x }$

Equations and Inequalities

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants and Applications

Analytic Geometry

Sequences, Series, Induction, and Probability

Review of Prerequisites

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Exam 2: Functions and Relations

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The graph of y = f (3x) is the graph of y = f (x) with a (choose one: vertical stretch, vertical shrink, horizontal stretch, horizontal shrink).

Evaluate the function for the indicated value. -Evaluate f(−1)f ( - 1 )f(−1) f(x)={9x≤−1∣x+1∣−1<x≤5−5x>5f ( x ) = \left\{ \begin{array} { c c } 9 & x \leq - 1 \\| x + 1 | & - 1 < x \leq 5 \\- 5 & x > 5\end{array} \right.f(x)=⎩⎨⎧​9∣x+1∣−5​x≤−1−1<x≤5x>5​

Evaluate the function for the given value of x. - f(x)=x3+6x,(f∘f)(3)= ? f ( x ) = x ^ { 3 } + 6 x , ( f \circ f ) ( 3 ) = \text { ? }f(x)=x3+6x,(f∘f)(3)= ?

Choose the one alternative that best completes the statement or answers the question. Graph the equation and identify the x- and y-intercepts. - 3x=−5y3 x = - 5 y3x=−5y

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The graph of a constant function defined by f(x) = b is a (horizontal/vertical) line.

Solve the problem. -Find the shortest distance from the origin to a point on the circle defined by x2+y2−14x−18y+121=0. x ^ { 2 } + y ^ { 2 } - 14 x - 18 y + 121 = 0 \text {. }x2+y2−14x−18y+121=0.

Write the equation in slope-intercept form. Then, graph the line using the slope and y-intercept. - −3x+5y=−15-3 x+5 y=-15−3x+5y=−15

The slope of a line is given. a. Determine the slope of a line parallel to the given line, if possible. b. Determine the slope of a line perpendicular to the given line, if possible. - m=85m = \frac { 8 } { 5 }m=58​

Write the given equation in the form (x−h)2+(y−k)2=r2( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }(x−h)2+(y−k)2=r2 . Identify the center and radius. - x2+y2−6x+6y−82=0x ^ { 2 } + y ^ { 2 } - 6 x + 6 y - 82 = 0x2+y2−6x+6y−82=0

Write an equation of the line satisfying the given conditions. -The line passes through (42, 17) and is parallel to y = 6.

Write an equation of the line satisfying the given conditions. Write the answer in standard form with no fractional coefficients. -Passes through (4,4)( 4,4 )(4,4) and is perpendicular to the line defined by −5x+4y=−6- 5 x + 4 y = - 6−5x+4y=−6

Use translations to graph the given function. - f(x)=∣x+1∣f ( x ) = | x + 1 |f(x)=∣x+1∣

Determine the center and radius of the circle. - (x−4)2+(y−8)2=9( x - 4 ) ^ { 2 } + ( y - 8 ) ^ { 2 } = 9(x−4)2+(y−8)2=9

Determine the domain and range of the function. -

Find an equation of the circle with the given characteristics. -Center (8,−7)( 8 , - 7 )(8,−7) and radius 3

Solve the problem. -A certain medicine is administered to animals based on the weight. The recommended dose is 4 mg per lb of the animal's weight. Construct a linear function and use it to determine what size animal Would require a 1,300-mg dose of the medicine.

In a rectangular coordinate system, the point where the x- and y-axes meet is called the________

Write a function based on the given parent function and the transformations in the given order. -Parent function y=1xy = \frac { 1 } { x }y=x1​ 1. Stretch vertically by a factor of 6. 2. Reflect across the x-axis. 3) Shift downward 9 units.

Write the domain in interval notation. - a(x)=8−xa ( x ) = \sqrt { 8 - x }a(x)=8−x​

Equations and Inequalities

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants and Applications

Analytic Geometry

Sequences, Series, Induction, and Probability

Review of Prerequisites

Filters

Evaluate the function for the indicated value. -Evaluate $f ( - 1 )$ $f ( x ) = \left\{ \begin{array} { c c } 9 & x \leq - 1 \\| x + 1 | & - 1 < x \leq 5 \\- 5 & x > 5\end{array} \right.$

Evaluate the function for the given value of x. - $f ( x ) = x ^ { 3 } + 6 x , ( f \circ f ) ( 3 ) = \text { ? }$

Choose the one alternative that best completes the statement or answers the question. Graph the equation and identify the x- and y-intercepts. - $3 x = - 5 y$

Solve the problem. -Find the shortest distance from the origin to a point on the circle defined by $x ^ { 2 } + y ^ { 2 } - 14 x - 18 y + 121 = 0 \text {. }$

Write the equation in slope-intercept form. Then, graph the line using the slope and y-intercept. - $-3 x+5 y=-15$

The slope of a line is given. a. Determine the slope of a line parallel to the given line, if possible. b. Determine the slope of a line perpendicular to the given line, if possible. - $m = \frac { 8 } { 5 }$

Write the given equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Identify the center and radius. - $x ^ { 2 } + y ^ { 2 } - 6 x + 6 y - 82 = 0$

Write an equation of the line satisfying the given conditions. Write the answer in standard form with no fractional coefficients. -Passes through $( 4,4 )$ and is perpendicular to the line defined by $- 5 x + 4 y = - 6$

Use translations to graph the given function. - $f ( x ) = | x + 1 |$

Determine the center and radius of the circle. - $( x - 4 ) ^ { 2 } + ( y - 8 ) ^ { 2 } = 9$

Find an equation of the circle with the given characteristics. -Center $( 8 , - 7 )$ and radius 3

Write a function based on the given parent function and the transformations in the given order. -Parent function $y = \frac { 1 } { x }$ 1. Stretch vertically by a factor of 6. 2. Reflect across the x-axis. 3) Shift downward 9 units.

Write the domain in interval notation. - $a ( x ) = \sqrt { 8 - x }$