Exam 2: Functions and Relations

Solve the problem. - \[\begin{array} { l } \text { Wse the graph of } y = f ( x ) \text { below to graph } y = 5 f ( x ) $Solve the problem. - \[\begin{array} { l } \text { Wse the graph of } y = f ( x ) \text { below to graph } y = 5 f ( x )$

(Multiple Choice)

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Question 61

Find the indicated function and write its domain in interval notation. - $s ( x ) = \frac { x - 5 } { x ^ { 2 } - 36 } , t ( x ) = \frac { x - 6 } { 5 - x } , ( s + t ) ( x ) = ?$

(Multiple Choice)

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Question 62

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Let c represent a positive real number. The graph of y = f (x - c) is the graph of y = f (x) shifted (up/down/left/right) c units.

(Short Answer)

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Question 63

Solve the problem. -At the Jumping Jack cookie factory, quality assurance inspectors remove broken or otherwise defective cookies from a moving conveyor belt prior to packaging. Based on past studies, the plant Manager knows that the inspectors eliminate 98% of the defective cookies at a conveyor belt speed Of 9 feet per minute. As the belt speed increases, the factory can produce more cookies per hour, but At the cost of lower quality of the packaged product. Inspectors collect only 60% of defective Cookies at a belt speed of 18 feet per minute. a. Find an equation of the line through the given points. Write the equation in slope-intercept form. Round The slope and y-intercept each to 1 decimal place. b. Use the equation from part (b) to predict the efficiency of the inspectors at a belt speed of 15 feet per Minute. Round to the nearest percent.

(Multiple Choice)

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Question 64

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Let c represent a positive real number. The graph of y = f (x + c) is the graph of y = f (x) shifted (up/down/left/right) c units.

(Short Answer)

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Question 65

Find the difference quotient and simplify. - $f ( x ) = - 3 x - 6$

(Multiple Choice)

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Question 66

Find the indicated function and write its domain in interval notation. - $m ( x ) = \sqrt { x + 2 } , n ( x ) = x - 3 , ( m \circ n ) ( x ) = \text { ? }$

(Multiple Choice)

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Question 67

Graph the function. - $t ( x ) = \left\{ \begin{array} { l } x - 1 , \quad \text { for } x > 0 \\- x ^ { 2 } , \text { for } x \leq 0\end{array} \right.$

(Multiple Choice)

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Question 68

Solve the problem. -If $a$ is $b$ plus nine, and $c$ is the square of $a$ , write $c$ as a function of $b$ .

(Multiple Choice)

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Question 69

Find the indicated function and write its domain in interval notation. - $f ( x ) = \frac { x } { x - 1 } , g ( x ) = \frac { 36 } { x ^ { 2 } - 64 } , ( f \circ g ) ( x ) = ?$

(Multiple Choice)

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Question 70

Write the domain in interval notation. - $p ( x ) = 7 x + 1 ; x \geq 0$

(Multiple Choice)

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Question 71

Use the graph of y = f (x) below to graph y = f (-x) -

(Multiple Choice)

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Question 72

Identify the set of values x for which y will be a real number. - $y = \sqrt { x - 8 }$

(Multiple Choice)

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Question 73

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -An equation of the form y = k where k is a constant represents the graph of a line.

(Short Answer)

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Question 74

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. - $x = y ^ { 4 } - y ^ { 6 }$

(Multiple Choice)

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Question 75

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -An equation written in the form y = mx + b is said to be written in - form.

(Short Answer)

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Question 76

Evaluate the function for the indicated value. -Evaluate $f ( - 12 )$ $f ( x ) = \left\{ \begin{array} { c c } 7 & x \leq - 2 \\| x + 1 | & - 2 < x \leq 4 \\- 5 & x > 4\end{array} \right.$

(Multiple Choice)

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Question 77

Determine the x- and y-intercepts for the given function. - $r ( x ) = | x - 8 |$

(Multiple Choice)

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Question 78

Write the word or phrase that best completes each statement or answers the question.Provide the missing information. -The function $f + g$ is defined by $( f + g ) ( x ) =$ ـــــــــــ $+$ ـــــــــ

(Short Answer)

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Question 79

The graph of y = f (x) is given. Graph the indicated function. -Graph $y = f ( - x ) - 4$

(Multiple Choice)

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Question 80

Solve the problem. - \[\begin{array} { l } \text { Wse the graph of } y = f ( x ) \text { below to graph } y = 5 f ( x ) $Solve the problem. - \[\begin{array} { l } \text { Wse the graph of } y = f ( x ) \text { below to graph } y = 5 f ( x )$

Find the indicated function and write its domain in interval notation. - $s ( x ) = \frac { x - 5 } { x ^ { 2 } - 36 } , t ( x ) = \frac { x - 6 } { 5 - x } , ( s + t ) ( x ) = ?$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Let c represent a positive real number. The graph of y = f (x - c) is the graph of y = f (x) shifted (up/down/left/right) c units.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Let c represent a positive real number. The graph of y = f (x + c) is the graph of y = f (x) shifted (up/down/left/right) c units.

Find the difference quotient and simplify. - $f ( x ) = - 3 x - 6$

Find the indicated function and write its domain in interval notation. - $m ( x ) = \sqrt { x + 2 } , n ( x ) = x - 3 , ( m \circ n ) ( x ) = \text { ? }$

Graph the function. - $t ( x ) = \left\{ \begin{array} { l } x - 1 , \quad \text { for } x > 0 \\- x ^ { 2 } , \text { for } x \leq 0\end{array} \right.$

Solve the problem. -If $a$ is $b$ plus nine, and $c$ is the square of $a$ , write $c$ as a function of $b$ .

Find the indicated function and write its domain in interval notation. - $f ( x ) = \frac { x } { x - 1 } , g ( x ) = \frac { 36 } { x ^ { 2 } - 64 } , ( f \circ g ) ( x ) = ?$

Write the domain in interval notation. - $p ( x ) = 7 x + 1 ; x \geq 0$

Use the graph of y = f (x) below to graph y = f (-x) -

Identify the set of values x for which y will be a real number. - $y = \sqrt { x - 8 }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -An equation of the form y = k where k is a constant represents the graph of a line.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. - $x = y ^ { 4 } - y ^ { 6 }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -An equation written in the form y = mx + b is said to be written in - form.

Evaluate the function for the indicated value. -Evaluate $f ( - 12 )$ $f ( x ) = \left\{ \begin{array} { c c } 7 & x \leq - 2 \\| x + 1 | & - 2 < x \leq 4 \\- 5 & x > 4\end{array} \right.$

Determine the x- and y-intercepts for the given function. - $r ( x ) = | x - 8 |$

Write the word or phrase that best completes each statement or answers the question.Provide the missing information. -The function $f + g$ is defined by $( f + g ) ( x ) =$ ـــــــــــ $+$ ـــــــــ

The graph of y = f (x) is given. Graph the indicated function. -Graph $y = f ( - x ) - 4$

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

Solve the problem. - \[\begin{array} { l } \text { Wse the graph of } y = f ( x ) \text { below to graph } y = 5 f ( x )

Find the indicated function and write its domain in interval notation. - s(x)=x−5x2−36,t(x)=x−65−x,(s+t)(x)=?s ( x ) = \frac { x - 5 } { x ^ { 2 } - 36 } , t ( x ) = \frac { x - 6 } { 5 - x } , ( s + t ) ( x ) = ?s(x)=x2−36x−5​,t(x)=5−xx−6​,(s+t)(x)=?

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Let c represent a positive real number. The graph of y = f (x - c) is the graph of y = f (x) shifted (up/down/left/right) c units.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Let c represent a positive real number. The graph of y = f (x + c) is the graph of y = f (x) shifted (up/down/left/right) c units.

Find the difference quotient and simplify. - f(x)=−3x−6f ( x ) = - 3 x - 6f(x)=−3x−6

Find the indicated function and write its domain in interval notation. - m(x)=x+2,n(x)=x−3,(m∘n)(x)= ? m ( x ) = \sqrt { x + 2 } , n ( x ) = x - 3 , ( m \circ n ) ( x ) = \text { ? }m(x)=x+2​,n(x)=x−3,(m∘n)(x)= ?

Graph the function. - t(x)={x−1, for x>0−x2, for x≤0t ( x ) = \left\{ \begin{array} { l } x - 1 , \quad \text { for } x > 0 \\- x ^ { 2 } , \text { for } x \leq 0\end{array} \right.t(x)={x−1, for x>0−x2, for x≤0​

Solve the problem. -If aaa is bbb plus nine, and ccc is the square of aaa , write ccc as a function of bbb .

Find the indicated function and write its domain in interval notation. - f(x)=xx−1,g(x)=36x2−64,(f∘g)(x)=?f ( x ) = \frac { x } { x - 1 } , g ( x ) = \frac { 36 } { x ^ { 2 } - 64 } , ( f \circ g ) ( x ) = ?f(x)=x−1x​,g(x)=x2−6436​,(f∘g)(x)=?

Write the domain in interval notation. - p(x)=7x+1;x≥0p ( x ) = 7 x + 1 ; x \geq 0p(x)=7x+1;x≥0

Use the graph of y = f (x) below to graph y = f (-x) -

Identify the set of values x for which y will be a real number. - y=x−8y = \sqrt { x - 8 }y=x−8​

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -An equation of the form y = k where k is a constant represents the graph of a line.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. - x=y4−y6x = y ^ { 4 } - y ^ { 6 }x=y4−y6

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -An equation written in the form y = mx + b is said to be written in - form.

Evaluate the function for the indicated value. -Evaluate f(−12)f ( - 12 )f(−12) f(x)={7x≤−2∣x+1∣−2<x≤4−5x>4f ( x ) = \left\{ \begin{array} { c c } 7 & x \leq - 2 \\| x + 1 | & - 2 < x \leq 4 \\- 5 & x > 4\end{array} \right.f(x)=⎩⎨⎧​7∣x+1∣−5​x≤−2−2<x≤4x>4​

Determine the x- and y-intercepts for the given function. - r(x)=∣x−8∣r ( x ) = | x - 8 |r(x)=∣x−8∣

Write the word or phrase that best completes each statement or answers the question.Provide the missing information. -The function f+gf + gf+g is defined by (f+g)(x)=( f + g ) ( x ) =(f+g)(x)= ـــــــــــ +++ ـــــــــ

The graph of y = f (x) is given. Graph the indicated function. -Graph y=f(−x)−4y = f ( - x ) - 4y=f(−x)−4

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

Solve the problem. - \[\begin{array} { l } \text { Wse the graph of } y = f ( x ) \text { below to graph } y = 5 f ( x ) $Solve the problem. - \[\begin{array} { l } \text { Wse the graph of } y = f ( x ) \text { below to graph } y = 5 f ( x )$

Find the indicated function and write its domain in interval notation. - $s ( x ) = \frac { x - 5 } { x ^ { 2 } - 36 } , t ( x ) = \frac { x - 6 } { 5 - x } , ( s + t ) ( x ) = ?$

Find the difference quotient and simplify. - $f ( x ) = - 3 x - 6$

Find the indicated function and write its domain in interval notation. - $m ( x ) = \sqrt { x + 2 } , n ( x ) = x - 3 , ( m \circ n ) ( x ) = \text { ? }$

Graph the function. - $t ( x ) = \left\{ \begin{array} { l } x - 1 , \quad \text { for } x > 0 \\- x ^ { 2 } , \text { for } x \leq 0\end{array} \right.$

Solve the problem. -If $a$ is $b$ plus nine, and $c$ is the square of $a$ , write $c$ as a function of $b$ .

Find the indicated function and write its domain in interval notation. - $f ( x ) = \frac { x } { x - 1 } , g ( x ) = \frac { 36 } { x ^ { 2 } - 64 } , ( f \circ g ) ( x ) = ?$

Write the domain in interval notation. - $p ( x ) = 7 x + 1 ; x \geq 0$

Identify the set of values x for which y will be a real number. - $y = \sqrt { x - 8 }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. - $x = y ^ { 4 } - y ^ { 6 }$

Evaluate the function for the indicated value. -Evaluate $f ( - 12 )$ $f ( x ) = \left\{ \begin{array} { c c } 7 & x \leq - 2 \\| x + 1 | & - 2 < x \leq 4 \\- 5 & x > 4\end{array} \right.$

Determine the x- and y-intercepts for the given function. - $r ( x ) = | x - 8 |$

Write the word or phrase that best completes each statement or answers the question.Provide the missing information. -The function $f + g$ is defined by $( f + g ) ( x ) =$ ـــــــــــ $+$ ـــــــــ

The graph of y = f (x) is given. Graph the indicated function. -Graph $y = f ( - x ) - 4$