Use the functions given by $f ( x ) = \frac { 1 } { 64 } x - 4$ and g(x) = x3 to find g-1 º f-1.

A) $4 \sqrt [ 3 ] { ( 4 - x ) }$ B) $- 4 \sqrt [ 3 ] { ( x + 4 ) }$ C) $- 4 \sqrt [ 3 ] { ( x - 4 ) }$ D) $4 \sqrt [ 3 ] { ( x - 4 ) }$ E) $4 \sqrt [ 3 ] { ( x + 4 ) }$ A) $4 \sqrt [ 3 ] { ( 4 - x ) }$ B) $- 4 \sqrt [ 3 ] { ( x + 4 ) }$ C) $- 4 \sqrt [ 3 ] { ( x - 4 ) }$ D) $4 \sqrt [ 3 ] { ( x - 4 ) }$ E) $4 \sqrt [ 3 ] { ( x + 4 ) }$

Evaluate S(3) if S(r) = 4πr2.

A) S(3) = 40π B) S(3) = 9π C) S(3) = 38π D) S(3) = 36π E) S(3) = 37π A) S(3) = 40π B) S(3) = 9π C) S(3) = 38π D) S(3) = 36π E) S(3) = 37π

Find the inverse function of f informally. F(x) = x4

A) $f ^ { - 1 } ( x ) = 4 \sqrt { x }$ B) $f ^ { - 1 } ( x ) = \sqrt [ 4 ] { x }$ C) $f ^ { - 1 } ( x ) = \frac { 1 } { \sqrt [ 4 ] { x } }$ D) $f ^ { - 1 } ( x ) = ( \sqrt [ 4 ] { x } ) ^ { 4 }$ E) $f ^ { - 1 } ( x ) = - \sqrt [ 4 ] { x }$ A) $f ^ { - 1 } ( x ) = 4 \sqrt { x }$ B) $f ^ { - 1 } ( x ) = \sqrt [ 4 ] { x }$ C) $f ^ { - 1 } ( x ) = \frac { 1 } { \sqrt [ 4 ] { x } }$ D) $f ^ { - 1 } ( x ) = ( \sqrt [ 4 ] { x } ) ^ { 4 }$ E) $f ^ { - 1 } ( x ) = - \sqrt [ 4 ] { x }$

An object is thrown upward from a height of 8 feet at a velocity of 72 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 - 72t + 8 B) s = -16t2 + 72t C) s = -16t2 + 72t - 8 D) s = -16t2 + 72t + 8 E) s = -16t2 - 72t - 8 A) s = -16t2 - 72t + 8 B) s = -16t2 + 72t C) s = -16t2 + 72t - 8 D) s = -16t2 + 72t + 8 E) s = -16t2 - 72t - 8

Exam 1: Functions and Their Graphs

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(4, $\frac { 8 } { 7 }$ ), m = 0

(Multiple Choice)

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Question 401

An overhead garage door has two springs, one on each side of the door (see figure).A force of $20$ pounds is required to stretch each spring 1 foot.Because of a pulley system, the springs stretch only one-half the distance the door travels.The door moves a total of $x = 18$ feet, and the springs are at their natural length when the door is open.Find the combined lifting force applied to the door by the springs when the door is closed.

(Multiple Choice)

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Question 402

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is odd. (8, -7)

(Multiple Choice)

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Question 403

Identify the parent function and the transformation shown in the graph.Write an equation for the function shown in the graph.

(Multiple Choice)

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Question 404

Which set of ordered pairs represents a function from P to Q? P = {5, 10, 15, 20} Q = {-1, 1, 3}

(Multiple Choice)

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Question 405

Write the equation of the line that passes through the point P (0, 0) and is perpendicular to the line y = - 2x + 10.

(Multiple Choice)

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Question 406

Find a mathematical model representing the statement.(Determine the constant of proportionality.) Z varies jointly as x and y. $( z = 128 \text { when } x = 4 \text { and } y = 8 . )$

(Multiple Choice)

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Question 407

Evaluate f(11) if $f ( x ) = \frac { | x | } { x }$ .

(Multiple Choice)

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Question 408

The following is the slope of line representing daily revenue y in term of time x in day.Use the slope to interpret any change in daily revenues for a one-day increase in time. The line has a slope of m = 500.

(Multiple Choice)

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Question 409

Use the functions given by $f ( x ) = \frac { 1 } { 64 } x - 4$ and g(x) = x³ to find g^-1 _º f^-1.

(Multiple Choice)

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Question 410

Evaluate S(3) if S(r) = 4πr².

(Multiple Choice)

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Question 411

Find the inverse function of f informally. F(x) = x⁴

(Multiple Choice)

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Question 412

Find $g \circ f$ . $f ( x ) = x - 9 \quad g ( x ) = x ^ { 2 }$

(Multiple Choice)

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Question 413

Approximate the coordinates of the points.

(Multiple Choice)

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Question 414

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

(Multiple Choice)

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Question 415

Find the coordinates of the point that is located 8 units below the x-axis and 3 units to the left of the y-axis.

(Multiple Choice)

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Question 416

Write the standard form of the equation of the circle with the given characteristics. center: (-5, -4); solution point: (-3, -7)

(Multiple Choice)

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Question 417

Consider the functions $f ( x ) = x ^ { 3 }$ and $g ( x ) = \sqrt { x }$ . Find $f / g$ .

(Multiple Choice)

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Question 418

Determine whether the function is one-to- one. Y = 3x

(Multiple Choice)

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Question 419

An object is thrown upward from a height of 8 feet at a velocity of 72 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 420

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(4, $\frac { 8 } { 7 }$ ), m = 0

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is odd. (8, -7)

Identify the parent function and the transformation shown in the graph.Write an equation for the function shown in the graph.

Which set of ordered pairs represents a function from P to Q? P = {5, 10, 15, 20} Q = {-1, 1, 3}

Write the equation of the line that passes through the point P (0, 0) and is perpendicular to the line y = - 2x + 10.

Find a mathematical model representing the statement.(Determine the constant of proportionality.) Z varies jointly as x and y. $( z = 128 \text { when } x = 4 \text { and } y = 8 . )$

Evaluate f(11) if $f ( x ) = \frac { | x | } { x }$ .

The following is the slope of line representing daily revenue y in term of time x in day.Use the slope to interpret any change in daily revenues for a one-day increase in time. The line has a slope of m = 500.

Use the functions given by $f ( x ) = \frac { 1 } { 64 } x - 4$ and g(x) = x³ to find g^-1 _º f^-1.

Evaluate S(3) if S(r) = 4πr².

Find the inverse function of f informally. F(x) = x⁴

Find $g \circ f$ . $f ( x ) = x - 9 \quad g ( x ) = x ^ { 2 }$

Approximate the coordinates of the points.

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

Find the coordinates of the point that is located 8 units below the x-axis and 3 units to the left of the y-axis.

Write the standard form of the equation of the circle with the given characteristics. center: (-5, -4); solution point: (-3, -7)

Consider the functions $f ( x ) = x ^ { 3 }$ and $g ( x ) = \sqrt { x }$ . Find $f / g$ .

Determine whether the function is one-to- one. Y = 3x

An object is thrown upward from a height of 8 feet at a velocity of 72 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.

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

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(4, 87\frac { 8 } { 7 }78​ ), m = 0

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is odd. ​ (8, -7) ​

Identify the parent function and the transformation shown in the graph.Write an equation for the function shown in the graph.

Which set of ordered pairs represents a function from P to Q? P = {5, 10, 15, 20} Q = {-1, 1, 3}

Write the equation of the line that passes through the point P (0, 0) and is perpendicular to the line y = - 2x + 10.

Find a mathematical model representing the statement.(Determine the constant of proportionality.) Z varies jointly as x and y. (z=128 when x=4 and y=8.)( z = 128 \text { when } x = 4 \text { and } y = 8 . )(z=128 when x=4 and y=8.)

Evaluate f(11) if f(x)=∣x∣xf ( x ) = \frac { | x | } { x }f(x)=x∣x∣​ .

The following is the slope of line representing daily revenue y in term of time x in day.Use the slope to interpret any change in daily revenues for a one-day increase in time. ​ The line has a slope of m = 500. ​

Use the functions given by f(x)=164x−4f ( x ) = \frac { 1 } { 64 } x - 4f(x)=641​x−4 and g(x) = x3 to find g-1 º f-1.

Evaluate S(3) if S(r) = 4πr2. ​

Find the inverse function of f informally. F(x) = x4

Find g∘fg \circ fg∘f . f(x)=x−9g(x)=x2f ( x ) = x - 9 \quad g ( x ) = x ^ { 2 }f(x)=x−9g(x)=x2

Approximate the coordinates of the points. ​

Use a graphing utility to graph the equation.Use a standard setting.Approximate any intercepts. y=xx+2y = x \sqrt { x + 2 }y=xx+2​

Find the coordinates of the point that is located 8 units below the x-axis and 3 units to the left of the y-axis. ​ ​

Write the standard form of the equation of the circle with the given characteristics. center: (-5, -4); solution point: (-3, -7)

Consider the functions f(x)=x3f ( x ) = x ^ { 3 }f(x)=x3 and g(x)=xg ( x ) = \sqrt { x }g(x)=x​ . Find f/gf / gf/g .

Determine whether the function is one-to- one. ​ Y = 3x ​

An object is thrown upward from a height of 8 feet at a velocity of 72 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. ​

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 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(4, $\frac { 8 } { 7 }$ ), m = 0

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is odd. (8, -7)

Find a mathematical model representing the statement.(Determine the constant of proportionality.) Z varies jointly as x and y. $( z = 128 \text { when } x = 4 \text { and } y = 8 . )$

Evaluate f(11) if $f ( x ) = \frac { | x | } { x }$ .

The following is the slope of line representing daily revenue y in term of time x in day.Use the slope to interpret any change in daily revenues for a one-day increase in time. The line has a slope of m = 500.

Use the functions given by $f ( x ) = \frac { 1 } { 64 } x - 4$ and g(x) = x³ to find g^-1 _º f^-1.

Evaluate S(3) if S(r) = 4πr².

Find the inverse function of f informally. F(x) = x⁴

Find $g \circ f$ . $f ( x ) = x - 9 \quad g ( x ) = x ^ { 2 }$

Approximate the coordinates of the points.

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

Find the coordinates of the point that is located 8 units below the x-axis and 3 units to the left of the y-axis.

Consider the functions $f ( x ) = x ^ { 3 }$ and $g ( x ) = \sqrt { x }$ . Find $f / g$ .

Determine whether the function is one-to- one. Y = 3x

An object is thrown upward from a height of 8 feet at a velocity of 72 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.