An object is thrown upward from a height of 6.4 feet at a velocity of 80 feet per second. Use the position equation s = -16t2 + v0t + s0 to select a function that represents the situation and select the graph of the function.

A) s = -16t2 + 80 - 6.4 B) s = -16t2 + 80t C) s = -16t2 - 80t - 6.4 D) s = -16t2 - 80t + 6.4 E) s = -16t2 + 80t + 6.4 A) s = -16t2 + 80 - 6.4 B) s = -16t2 + 80t C) s = -16t2 - 80t - 6.4 D) s = -16t2 - 80t + 6.4 E) s = -16t2 + 80t + 6.4

Use the functions given by $f ( x ) = \frac { 1 } { 8 } x - 5$ and g(x) = x3 to find (f-1 º f-1)(-5).

A) 36 B) 44 C) 40 D) 38 E) 42 A) 36 B) 44 C) 40 D) 38 E) 42

Evaluate the function $f ( x ) = \left\{ \begin{array} { c } 4 x - 2 , x 1 \end{array} \right.$ at $f \left( - \frac { 1 } { 2 } \right)$ .

A) $f \left( - \frac { 1 } { 2 } \right) = - 10$ B) $f \left( - \frac { 1 } { 2 } \right) = 10$ C) $f \left( - \frac { 1 } { 2 } \right) = - 7$ D) $f \left( - \frac { 1 } { 2 } \right) = - 4$ E) $f \left( - \frac { 1 } { 2 } \right) = 7$ A) $f \left( - \frac { 1 } { 2 } \right) = - 10$ B) $f \left( - \frac { 1 } { 2 } \right) = 10$ C) $f \left( - \frac { 1 } { 2 } \right) = - 7$ D) $f \left( - \frac { 1 } { 2 } \right) = - 4$ E) $f \left( - \frac { 1 } { 2 } \right) = 7$

Find the difference quotient and simplify your answer. F(x) = 5x - x2, $\frac { f ( 6 + h ) - f ( 6 ) } { h }$ , h$\neq$ 0

A) $\frac { f ( 6 + h ) - f ( 6 ) } { h } = - h - 6$ , h $\neq$ 0 B) $\frac { f ( 6 + h ) - f ( 6 ) } { h } = - h - 4$ , h $\neq$ 0 C) $\frac { f ( 6 + h ) - f ( 6 ) } { h } = - h - 3$ , h $\neq$ 0 D) $\frac { f ( 6 + h ) - f ( 6 ) } { h } = - h - 7$ , h $\neq$ 0 E) $\frac { f ( 6 + h ) - f ( 6 ) } { h } = - h - 5$ , h$\neq$ 0 A) $\frac { f ( 6 + h ) - f ( 6 ) } { h } = - h - 6$ , h $\neq$ 0 B) $\frac { f ( 6 + h ) - f ( 6 ) } { h } = - h - 4$ , h $\neq$ 0 C) $\frac { f ( 6 + h ) - f ( 6 ) } { h } = - h - 3$ , h $\neq$ 0 D) $\frac { f ( 6 + h ) - f ( 6 ) } { h } = - h - 7$ , h $\neq$ 0 E) $\frac { f ( 6 + h ) - f ( 6 ) } { h } = - h - 5$ , h$\neq$ 0

Exam 1: Functions and Their Graphs

The graph shows the numbers of performers who were elected to the Rock and Roll Hall of Fame from 1991 through 2008.Describe any trends in the data.From these trends, predict the number of performers elected in 2009.

(Multiple Choice)

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Question 81

Find the graph of the equation. $f ( x ) = \sqrt { 3 x - 4 }$

(Multiple Choice)

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Question 82

An object is thrown upward from a height of 6.4 feet at a velocity of 80 feet per second. Use the position equation s = -16t² + v₀t + s₀ to select a function that represents the situation and select the graph of the function.

(Multiple Choice)

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Question 83

Let the function $f$ be defined by the equation $y = f ( x )$ , where $x$ and $f ( x )$ are real numbers.Find the domain of the function $f ( x ) = \sqrt { 6 x ^ { 2 } + 16 }$

(Multiple Choice)

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Question 84

Use the given graph of f to select the graph for following function. $y = \frac { 1 } { 2 } f ( x )$ $Use the given graph of f to select the graph for following function. y = \frac { 1 } { 2 } f ( x )$

(Multiple Choice)

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Question 85

Find the zeros of the function algebraically. $f ( x ) = 2 x ^ { 2 } - 9 x - 35$

(Multiple Choice)

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Question 86

Use the functions given by $f ( x ) = \frac { 1 } { 8 } x - 5$ and g(x) = x³ to find (f^-1 _º f^-1)(-5).

(Multiple Choice)

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Question 87

Use a graphing utility to graph the equation.Use a standard setting.Approximate any intercepts. $y = x ^ { 2 } - 2 x$

(Multiple Choice)

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Question 88

On a yardstick with scales in inches and centimeters, you notice that 11 inches is approximately the same length as 33 centimeters.Use this information to find a mathematical model that relates centimeters y to inches x.Then use the model to find the numbers of centimeters in 60 inches and 70 inches.(Round your answer to one decimal place.)

(Multiple Choice)

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Question 89

Determine algebraically whether f and g are inverse functions. f(x) = 5x - 3 $g ( x ) = \frac { x + 3 } { 5 }$

(Multiple Choice)

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Question 90

Evaluate the function $f ( x ) = \left\{ \begin{array} { c } 4 x - 2 , x < - 1 \\7 , \quad - 1 \leq x \leq 1 \\x ^ { 2 } , x > 1\end{array} \right.$ at $f \left( - \frac { 1 } { 2 } \right)$ .

(Multiple Choice)

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Question 91

The graphs of $f ( x ) = | x | + 5$ and $f ( x ) = | - x | + 5$ are identical.

(True/False)

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Question 92

Find the slope of the line passing through the given pair of points. (0, 9), (2, 0)

(Multiple Choice)

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Question 93

Find the coordinates of the vertices of the polygon in its new position. Original coordinates of vertices: (6, 5), (3, 2), (4, 2), (5, 2) Shift: six units downward, two units to the left

(Multiple Choice)

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Question 94

Find $f \circ g$ and the domain of the composite function. $f ( x ) = \sqrt { x + 5 } , g ( x ) = x ^ { 2 }$

(Multiple Choice)

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Question 95

Find the difference quotient and simplify your answer. F(x) = 5x - x², $\frac { f ( 6 + h ) - f ( 6 ) } { h }$ , h $\neq$ 0

(Multiple Choice)

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Question 96

Select the graph of the function and find the zeros of the function. $f ( x ) = 7 + \frac { 13 } { x }$

(Multiple Choice)

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Question 97

Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope m.Select correct answer for the line. P(0, -7), m = 8

(Multiple Choice)

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Question 98

Let f (x) = 2x + 1, g (x) = 3x - 2.Find the function. $( f - g ) ( x )$ Please give the answer as a simplified expression (not an equation).

(Short Answer)

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Question 99

Find a mathematical model for the verbal statement: "Q is jointly proportional to the cube of h and the square root of m."

(Multiple Choice)

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Question 100

The graph shows the numbers of performers who were elected to the Rock and Roll Hall of Fame from 1991 through 2008.Describe any trends in the data.From these trends, predict the number of performers elected in 2009.

Find the graph of the equation. $f ( x ) = \sqrt { 3 x - 4 }$

An object is thrown upward from a height of 6.4 feet at a velocity of 80 feet per second. Use the position equation s = -16t² + v₀t + s₀ to select a function that represents the situation and select the graph of the function.

Let the function $f$ be defined by the equation $y = f ( x )$ , where $x$ and $f ( x )$ are real numbers.Find the domain of the function $f ( x ) = \sqrt { 6 x ^ { 2 } + 16 }$

Use the given graph of f to select the graph for following function. $y = \frac { 1 } { 2 } f ( x )$ $Use the given graph of f to select the graph for following function. y = \frac { 1 } { 2 } f ( x )$

Find the zeros of the function algebraically. $f ( x ) = 2 x ^ { 2 } - 9 x - 35$

Use the functions given by $f ( x ) = \frac { 1 } { 8 } x - 5$ and g(x) = x³ to find (f^-1 _º f^-1)(-5).

Use a graphing utility to graph the equation.Use a standard setting.Approximate any intercepts. $y = x ^ { 2 } - 2 x$

Determine algebraically whether f and g are inverse functions. f(x) = 5x - 3 $g ( x ) = \frac { x + 3 } { 5 }$

Evaluate the function $f ( x ) = \left\{ \begin{array} { c } 4 x - 2 , x < - 1 \\7 , \quad - 1 \leq x \leq 1 \\x ^ { 2 } , x > 1\end{array} \right.$ at $f \left( - \frac { 1 } { 2 } \right)$ .

The graphs of $f ( x ) = | x | + 5$ and $f ( x ) = | - x | + 5$ are identical.

Find the slope of the line passing through the given pair of points. (0, 9), (2, 0)

Find the coordinates of the vertices of the polygon in its new position. Original coordinates of vertices: (6, 5), (3, 2), (4, 2), (5, 2) Shift: six units downward, two units to the left

Find $f \circ g$ and the domain of the composite function. $f ( x ) = \sqrt { x + 5 } , g ( x ) = x ^ { 2 }$

Find the difference quotient and simplify your answer. F(x) = 5x - x², $\frac { f ( 6 + h ) - f ( 6 ) } { h }$ , h $\neq$ 0

Select the graph of the function and find the zeros of the function. $f ( x ) = 7 + \frac { 13 } { x }$

Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope m.Select correct answer for the line. P(0, -7), m = 8

Let f (x) = 2x + 1, g (x) = 3x - 2.Find the function. $( f - g ) ( x )$ Please give the answer as a simplified expression (not an equation).

Find a mathematical model for the verbal statement: "Q is jointly proportional to the cube of h and the square root of m."

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Exam 1: Functions and Their Graphs

The graph shows the numbers of performers who were elected to the Rock and Roll Hall of Fame from 1991 through 2008.Describe any trends in the data.From these trends, predict the number of performers elected in 2009.

Find the graph of the equation. f(x)=3x−4f ( x ) = \sqrt { 3 x - 4 }f(x)=3x−4​

An object is thrown upward from a height of 6.4 feet at a velocity of 80 feet per second. Use the position equation s = -16t2 + v0t + s0 to select a function that represents the situation and select the graph of the function. ​

Let the function fff be defined by the equation y=f(x)y = f ( x )y=f(x) , where xxx and f(x)f ( x )f(x) are real numbers.Find the domain of the function f(x)=6x2+16f ( x ) = \sqrt { 6 x ^ { 2 } + 16 }f(x)=6x2+16​

Use the given graph of f to select the graph for following function. y=12f(x)y = \frac { 1 } { 2 } f ( x )y=21​f(x)

Find the zeros of the function algebraically. f(x)=2x2−9x−35f ( x ) = 2 x ^ { 2 } - 9 x - 35f(x)=2x2−9x−35

Use the functions given by f(x)=18x−5f ( x ) = \frac { 1 } { 8 } x - 5f(x)=81​x−5 and g(x) = x3 to find (f-1 º f-1)(-5).

Use a graphing utility to graph the equation.Use a standard setting.Approximate any intercepts. y=x2−2xy = x ^ { 2 } - 2 xy=x2−2x

Determine algebraically whether f and g are inverse functions. f(x) = 5x - 3 g(x)=x+35g ( x ) = \frac { x + 3 } { 5 }g(x)=5x+3​

Evaluate the function f(x)={4x−2,x<−17,−1≤x≤1x2,x>1f ( x ) = \left\{ \begin{array} { c } 4 x - 2 , x < - 1 \\7 , \quad - 1 \leq x \leq 1 \\x ^ { 2 } , x > 1\end{array} \right.f(x)=⎩⎨⎧​4x−2,x<−17,−1≤x≤1x2,x>1​ at f(−12)f \left( - \frac { 1 } { 2 } \right)f(−21​) .

The graphs of f(x)=∣x∣+5f ( x ) = | x | + 5f(x)=∣x∣+5 and f(x)=∣−x∣+5f ( x ) = | - x | + 5f(x)=∣−x∣+5 are identical.

Find the slope of the line passing through the given pair of points. (0, 9), (2, 0)

Find the coordinates of the vertices of the polygon in its new position. ​ Original coordinates of vertices: (6, 5), (3, 2), (4, 2), (5, 2)​ Shift: six units downward, two units to the left ​

Find f∘gf \circ gf∘g and the domain of the composite function. f(x)=x+5,g(x)=x2f ( x ) = \sqrt { x + 5 } , g ( x ) = x ^ { 2 }f(x)=x+5​,g(x)=x2

Find the difference quotient and simplify your answer. F(x) = 5x - x2, f(6+h)−f(6)h\frac { f ( 6 + h ) - f ( 6 ) } { h }hf(6+h)−f(6)​ , h ≠\neq= 0

Select the graph of the function and find the zeros of the function. f(x)=7+13xf ( x ) = 7 + \frac { 13 } { x }f(x)=7+x13​

Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope m.Select correct answer for the line. P(0, -7), m = 8

Let f (x) = 2x + 1, g (x) = 3x - 2.Find the function. ​ (f−g)(x)( f - g ) ( x )(f−g)(x) ​ Please give the answer as a simplified expression (not an equation).

Find a mathematical model for the verbal statement: "Q is jointly proportional to the cube of h and the square root of m."

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Find the graph of the equation. $f ( x ) = \sqrt { 3 x - 4 }$

An object is thrown upward from a height of 6.4 feet at a velocity of 80 feet per second. Use the position equation s = -16t² + v₀t + s₀ to select a function that represents the situation and select the graph of the function.

Let the function $f$ be defined by the equation $y = f ( x )$ , where $x$ and $f ( x )$ are real numbers.Find the domain of the function $f ( x ) = \sqrt { 6 x ^ { 2 } + 16 }$

Use the given graph of f to select the graph for following function. $y = \frac { 1 } { 2 } f ( x )$ $Use the given graph of f to select the graph for following function. y = \frac { 1 } { 2 } f ( x )$

Find the zeros of the function algebraically. $f ( x ) = 2 x ^ { 2 } - 9 x - 35$

Use the functions given by $f ( x ) = \frac { 1 } { 8 } x - 5$ and g(x) = x³ to find (f^-1 _º f^-1)(-5).

Use a graphing utility to graph the equation.Use a standard setting.Approximate any intercepts. $y = x ^ { 2 } - 2 x$

Determine algebraically whether f and g are inverse functions. f(x) = 5x - 3 $g ( x ) = \frac { x + 3 } { 5 }$

Evaluate the function $f ( x ) = \left\{ \begin{array} { c } 4 x - 2 , x < - 1 \\7 , \quad - 1 \leq x \leq 1 \\x ^ { 2 } , x > 1\end{array} \right.$ at $f \left( - \frac { 1 } { 2 } \right)$ .

The graphs of $f ( x ) = | x | + 5$ and $f ( x ) = | - x | + 5$ are identical.

Find the coordinates of the vertices of the polygon in its new position. Original coordinates of vertices: (6, 5), (3, 2), (4, 2), (5, 2) Shift: six units downward, two units to the left

Find $f \circ g$ and the domain of the composite function. $f ( x ) = \sqrt { x + 5 } , g ( x ) = x ^ { 2 }$

Find the difference quotient and simplify your answer. F(x) = 5x - x², $\frac { f ( 6 + h ) - f ( 6 ) } { h }$ , h $\neq$ 0

Select the graph of the function and find the zeros of the function. $f ( x ) = 7 + \frac { 13 } { x }$

Let f (x) = 2x + 1, g (x) = 3x - 2.Find the function. $( f - g ) ( x )$ Please give the answer as a simplified expression (not an equation).