Exam 2: Functions and Relations

Write the word or phrase that best completes each statement or answers the question. - $\text { Consider the function } z = \{ ( 9 , - 5 ) , ( - 7,3 ) , ( - 1,9 ) \} \text {. Find the function value } z ( - 7 ) \text {. }$

(Short Answer)

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Question 21

Evaluate the function for the indicated value. -Evaluate $f ( 3 )$ $f ( x ) = \left\{ \begin{array} { c c } 7 & x \leq - 1 \\| x + 1 | & - 1 < x \leq 3 \\- 5 & x > 3\end{array} \right.$

(Multiple Choice)

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Question 22

Find the center of a circle if a diameter of the circle has the given endpoints. - $( - 1 , - 6 )$ and $( - 7 , - 2 )$ .

(Multiple Choice)

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Question 23

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given a function defined by y = f (x), to find the -intercept, evaluate f (0).

(Short Answer)

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Question 24

Evaluate the function for the given value of x. - $f ( x ) = x ^ { 3 } - 4 x , g ( x ) = \sqrt { 5 x } , h ( x ) = 4 x + 5 , ( f \circ h \circ g ) ( 5 ) = \text { ? }$

(Multiple Choice)

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Question 25

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The standard form of an equation of a circle with center (h, k) and radius r is given by .

(Short Answer)

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Question 26

Evaluate the step function defined by $f ( x ) = \operatorname { int } ( x )$ or the given value of x. -f (-1.9)

(Multiple Choice)

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Question 27

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The slope of a vertical line is .

(Short Answer)

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Question 28

Write the equation in standard form: $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Then, if possible, identify the center and radius of the circle. If the equation represents a degenerate case, give the solution set. - $x ^ { 2 } + y ^ { 2 } - 4 x + 2 y + 5 = 0$

(Multiple Choice)

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Question 29

Determine the slope of the line passing through the given points. - $( 1 , - 1 )$ and $( - 8 , - 3 )$

(Multiple Choice)

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Question 30

Write the equation in standard form to find the center and radius of the circle. Then sketch the graph. - $x ^ { 2 } + y ^ { 2 } - 6 x + 5 = 0$

(Multiple Choice)

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Question 31

Evaluate as indicated. -Let $f ( x ) = 7 x - 2$ . Find $f ( m - 6 )$ and simplify.

(Multiple Choice)

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Question 32

Choose the one alternative that best completes the statement or answers the question. Find (f + g)(x) and identify the graph of f + g. - $f ( x ) = | x |$ and $g ( x ) = - 3$

(Multiple Choice)

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Question 33

Use the given information to a. Graph the function. b. Write the domain in interval notation. c. Write the range in interval notation. - $f ( x ) = \left\{ \begin{array} { l l } | x | & \text { for } x < 4 \\ - x & \text { for } x \geq 4 \end{array} \right.$

(Multiple Choice)

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Question 34

Solve the problem. -The function given by $y = f ( x )$ shows the value of $\$ 6,000$ invested at $5 \%$ interest compounded continuously, $x$ years after the money was originally invested. Find the average amount earned per year between the 25 th year and 30 th year. $Solve the problem. -The function given by y = f ( x ) shows the value of \$ 6,000 invested at 5 \% interest compounded continuously, x years after the money was originally invested. Find the average amount earned per year between the 25 th year and 30 th year.$

(Multiple Choice)

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Question 35

Write the equation in slope-intercept form and determine the slope and y-intercept. - $- 2 x = - 3 y - 6$

(Multiple Choice)

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Question 36

Find and simplify f (x + h). - $f ( x ) = - 3 x ^ { 2 } + 2 x + 1$

(Multiple Choice)

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Question 37

Graph the function. - $r ( x ) = \left\{ \begin{array} { l l } - 3 & \text { for } - 4 \leq x < 0 \\ 2 & \text { for } 0 \leq x < 2 \\ - 2 & \text { for } x \geq 2 \end{array} \right.$

(Multiple Choice)

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Question 38

Find the indicated function and write its domain in interval notation. - $p ( x ) = x ^ { 2 } + 6 x , q ( x ) = \sqrt { 4 - x } , \left( \frac { q } { p } \right) ( x ) =$ ?

(Multiple Choice)

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Question 39

Determine whether the relation defines y as a function of x. -

(Multiple Choice)

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Question 40

Write the word or phrase that best completes each statement or answers the question. - $\text { Consider the function } z = \{ ( 9 , - 5 ) , ( - 7,3 ) , ( - 1,9 ) \} \text {. Find the function value } z ( - 7 ) \text {. }$

Evaluate the function for the indicated value. -Evaluate $f ( 3 )$ $f ( x ) = \left\{ \begin{array} { c c } 7 & x \leq - 1 \\| x + 1 | & - 1 < x \leq 3 \\- 5 & x > 3\end{array} \right.$

Find the center of a circle if a diameter of the circle has the given endpoints. - $( - 1 , - 6 )$ and $( - 7 , - 2 )$ .

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given a function defined by y = f (x), to find the -intercept, evaluate f (0).

Evaluate the function for the given value of x. - $f ( x ) = x ^ { 3 } - 4 x , g ( x ) = \sqrt { 5 x } , h ( x ) = 4 x + 5 , ( f \circ h \circ g ) ( 5 ) = \text { ? }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The standard form of an equation of a circle with center (h, k) and radius r is given by .

Evaluate the step function defined by $f ( x ) = \operatorname { int } ( x )$ or the given value of x. -f (-1.9)

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The slope of a vertical line is .

Write the equation in standard form: $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Then, if possible, identify the center and radius of the circle. If the equation represents a degenerate case, give the solution set. - $x ^ { 2 } + y ^ { 2 } - 4 x + 2 y + 5 = 0$

Determine the slope of the line passing through the given points. - $( 1 , - 1 )$ and $( - 8 , - 3 )$

Write the equation in standard form to find the center and radius of the circle. Then sketch the graph. - $x ^ { 2 } + y ^ { 2 } - 6 x + 5 = 0$

Evaluate as indicated. -Let $f ( x ) = 7 x - 2$ . Find $f ( m - 6 )$ and simplify.

Choose the one alternative that best completes the statement or answers the question. Find (f + g)(x) and identify the graph of f + g. - $f ( x ) = | x |$ and $g ( x ) = - 3$

Use the given information to a. Graph the function. b. Write the domain in interval notation. c. Write the range in interval notation. - $f ( x ) = \left\{ \begin{array} { l l } | x | & \text { for } x < 4 \\ - x & \text { for } x \geq 4 \end{array} \right.$

Write the equation in slope-intercept form and determine the slope and y-intercept. - $- 2 x = - 3 y - 6$

Find and simplify f (x + h). - $f ( x ) = - 3 x ^ { 2 } + 2 x + 1$

Graph the function. - $r ( x ) = \left\{ \begin{array} { l l } - 3 & \text { for } - 4 \leq x < 0 \\ 2 & \text { for } 0 \leq x < 2 \\ - 2 & \text { for } x \geq 2 \end{array} \right.$

Find the indicated function and write its domain in interval notation. - $p ( x ) = x ^ { 2 } + 6 x , q ( x ) = \sqrt { 4 - x } , \left( \frac { q } { p } \right) ( x ) =$ ?

Determine whether the relation defines y as a function of 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

Evaluate the function for the indicated value. -Evaluate f(3)f ( 3 )f(3) f(x)={7x≤−1∣x+1∣−1<x≤3−5x>3f ( x ) = \left\{ \begin{array} { c c } 7 & x \leq - 1 \\| x + 1 | & - 1 < x \leq 3 \\- 5 & x > 3\end{array} \right.f(x)=⎩⎨⎧​7∣x+1∣−5​x≤−1−1<x≤3x>3​

Find the center of a circle if a diameter of the circle has the given endpoints. - (−1,−6)( - 1 , - 6 )(−1,−6) and (−7,−2)( - 7 , - 2 )(−7,−2) .

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given a function defined by y = f (x), to find the -intercept, evaluate f (0).

Evaluate the function for the given value of x. - f(x)=x3−4x,g(x)=5x,h(x)=4x+5,(f∘h∘g)(5)= ? f ( x ) = x ^ { 3 } - 4 x , g ( x ) = \sqrt { 5 x } , h ( x ) = 4 x + 5 , ( f \circ h \circ g ) ( 5 ) = \text { ? }f(x)=x3−4x,g(x)=5x​,h(x)=4x+5,(f∘h∘g)(5)= ?

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The standard form of an equation of a circle with center (h, k) and radius r is given by .

Evaluate the step function defined by f(x)=int⁡(x)f ( x ) = \operatorname { int } ( x )f(x)=int(x) or the given value of x. -f (-1.9)

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The slope of a vertical line is .

Determine the slope of the line passing through the given points. - (1,−1)( 1 , - 1 )(1,−1) and (−8,−3)( - 8 , - 3 )(−8,−3)

Write the equation in standard form to find the center and radius of the circle. Then sketch the graph. - x2+y2−6x+5=0x ^ { 2 } + y ^ { 2 } - 6 x + 5 = 0x2+y2−6x+5=0

Evaluate as indicated. -Let f(x)=7x−2f ( x ) = 7 x - 2f(x)=7x−2 . Find f(m−6)f ( m - 6 )f(m−6) and simplify.

Choose the one alternative that best completes the statement or answers the question. Find (f + g)(x) and identify the graph of f + g. - f(x)=∣x∣f ( x ) = | x |f(x)=∣x∣ and g(x)=−3g ( x ) = - 3g(x)=−3

Solve the problem. -The function given by y=f(x)y = f ( x )y=f(x) shows the value of $6,000\$ 6,000$6,000 invested at 5%5 \%5% interest compounded continuously, xxx years after the money was originally invested. Find the average amount earned per year between the 25 th year and 30 th year.

Write the equation in slope-intercept form and determine the slope and y-intercept. - −2x=−3y−6- 2 x = - 3 y - 6−2x=−3y−6

Find and simplify f (x + h). - f(x)=−3x2+2x+1f ( x ) = - 3 x ^ { 2 } + 2 x + 1f(x)=−3x2+2x+1

Find the indicated function and write its domain in interval notation. - p(x)=x2+6x,q(x)=4−x,(qp)(x)=p ( x ) = x ^ { 2 } + 6 x , q ( x ) = \sqrt { 4 - x } , \left( \frac { q } { p } \right) ( x ) =p(x)=x2+6x,q(x)=4−x​,(pq​)(x)= ?

Determine whether the relation defines y as a function of 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 $f ( 3 )$ $f ( x ) = \left\{ \begin{array} { c c } 7 & x \leq - 1 \\| x + 1 | & - 1 < x \leq 3 \\- 5 & x > 3\end{array} \right.$

Find the center of a circle if a diameter of the circle has the given endpoints. - $( - 1 , - 6 )$ and $( - 7 , - 2 )$ .

Evaluate the function for the given value of x. - $f ( x ) = x ^ { 3 } - 4 x , g ( x ) = \sqrt { 5 x } , h ( x ) = 4 x + 5 , ( f \circ h \circ g ) ( 5 ) = \text { ? }$

Evaluate the step function defined by $f ( x ) = \operatorname { int } ( x )$ or the given value of x. -f (-1.9)

Determine the slope of the line passing through the given points. - $( 1 , - 1 )$ and $( - 8 , - 3 )$

Write the equation in standard form to find the center and radius of the circle. Then sketch the graph. - $x ^ { 2 } + y ^ { 2 } - 6 x + 5 = 0$

Evaluate as indicated. -Let $f ( x ) = 7 x - 2$ . Find $f ( m - 6 )$ and simplify.

Choose the one alternative that best completes the statement or answers the question. Find (f + g)(x) and identify the graph of f + g. - $f ( x ) = | x |$ and $g ( x ) = - 3$

Write the equation in slope-intercept form and determine the slope and y-intercept. - $- 2 x = - 3 y - 6$

Find and simplify f (x + h). - $f ( x ) = - 3 x ^ { 2 } + 2 x + 1$

Find the indicated function and write its domain in interval notation. - $p ( x ) = x ^ { 2 } + 6 x , q ( x ) = \sqrt { 4 - x } , \left( \frac { q } { p } \right) ( x ) =$ ?