Find (fF1F1F1S1?F1F1F10g)(x). $f ( x ) = 4 x ^ { 2 } - 8 x$ $g ( x ) = - 7 - x$

A) $( f / g ) ( x ) = \frac { 4 x ^ { 2 } - 8 x } { - 7 - x } , x \neq 7$ B) $( f / g ) ( x ) = \frac { 4 x ^ { 2 } - 8 x } { - 7 - x } , x \neq - 7$ C) $( f / g ) ( x ) = \frac { 4 x ^ { 2 } - 8 x } { - 7 - x } , x \neq 0$ D) $( f / g ) ( x ) = \frac { 4 x - 8 } { - 7 } , x \neq 0$ E) $( f / g ) ( x ) = - \frac { 4 x ^ { 2 } } { 7 } + 8 , x \neq 0$ A) $( f / g ) ( x ) = \frac { 4 x ^ { 2 } - 8 x } { - 7 - x } , x \neq 7$ B) $( f / g ) ( x ) = \frac { 4 x ^ { 2 } - 8 x } { - 7 - x } , x \neq - 7$ C) $( f / g ) ( x ) = \frac { 4 x ^ { 2 } - 8 x } { - 7 - x } , x \neq 0$ D) $( f / g ) ( x ) = \frac { 4 x - 8 } { - 7 } , x \neq 0$ E) $( f / g ) ( x ) = - \frac { 4 x ^ { 2 } } { 7 } + 8 , x \neq 0$

Exam 3: Functions and Graphs

Use the intercept form to find the equation of the line with the given intercepts. The intercept form of the equation of a line with intercepts (a, 0) and (0, b) is $\frac { x } { a } + \frac { y } { b } = 1 , a \neq 0 , b \neq 0$ $x$ -intercept: $( - 4,0 ) \quad y$ -intercept: $( 0,1 )$

(Multiple Choice)

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Question 21

Use the graph of $f ( x ) = x ^ { 3 } - 3 x ^ { 2 }$ to write an equation for the function $g$ . $Use the graph of f ( x ) = x ^ { 3 } - 3 x ^ { 2 } to write an equation for the function g .$ $Use the graph of f ( x ) = x ^ { 3 } - 3 x ^ { 2 } to write an equation for the function g .$

(Multiple Choice)

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Question 22

Use the graph of the function to find the domain and range of f.

(Multiple Choice)

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Question 23

A car was purchased for $42,000. Assuming the car depreciates at a rate of $5040 per year (straight-line depreciation) for the first 5 years, write the value v of the car as a function of the time t (measured in years) for $0 \leq t \leq 5$

(Multiple Choice)

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Question 24

Describe the sequence of transformation from $f ( x ) = x ^ { 2 }$ to $g ( x )$ if $g ( x ) = ( x - 6 ) ^ { 2 } - 7$

(Multiple Choice)

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Question 25

Find $g \circ f.$ f (x) = x + 4 g (x) = x2

(Multiple Choice)

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Question 26

Use a graphing utility to graph the function and approximate (to two decimal places) any relative minimum or relative maximum values. f (x) = x3 - x2 - 2x - 1

(Multiple Choice)

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Question 27

Decide whether the function is even, odd, or neither. $g ( x ) = x ^ { 3 } - 5 x$

(Multiple Choice)

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Question 28

Consider the graph of $g ( x ) = \sqrt { x }.$ Use your knowledge of rigid and nonrigid transformations to write an equation for the following descriptions. The graph of $g$ is reflected in the x-axis, shifted eight units to the right, and shifted nine unit downward.

(Multiple Choice)

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Question 29

Plot the points and find the slope of the line passing through the pair of points. (0, 4), (5, 2)

(Multiple Choice)

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Question 30

An open box is to be made from a square piece of cardboard having dimensions 32 inches by 32 inches by cutting out squares of area $x ^ { 2 }$ from each corner as shown in the figure below. Express the volume V of the box as a function of x. $An open box is to be made from a square piece of cardboard having dimensions 32 inches by 32 inches by cutting out squares of area x ^ { 2 } from each corner as shown in the figure below. Express the volume V of the box as a function of x. 32 - 2 x 32 - 2 x$ $32 - 2 x$ $32 - 2 x$

(Multiple Choice)

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Question 31

Use a graphing utility to graph the function, approximate the relative minimum or maximum of the function, and estimate the open intervals on which the function is increasing or decreasing. $f ( x ) = x ^ { 2 } - 4 x + 1$

(Multiple Choice)

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Question 32

Find (fg)(x). $f ( x ) = \sqrt { 2 x }$ $g ( x ) = \sqrt { - x + 3 }$

(Multiple Choice)

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Question 33

Sketch the graph of the function below. $f ( x ) = \sqrt { - x + 3 }$

(Multiple Choice)

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Question 34

Find $x$ such that the distance between the point $( - 2,5 )$ and $( x , 17 )$ is 15.

(Multiple Choice)

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Question 35

Use the graph of $f ( x ) = x ^ { 3 }$ to write equations for the functions whose graphs are shown. $Use the graph of f ( x ) = x ^ { 3 } to write equations for the functions whose graphs are shown.$

(Multiple Choice)

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Question 36

The marketing department of a company estimates that the demand for a product is given by $p = 180 - 0.0001 x,$ where $p$ is the price per unit and $x$ is the number of units. The cost $C$ of producing $x$ units is given by $C = 450,000 + 50 x,$ and the profit $P$ for producing and selling $x$ units is given by $P = R - C = x p - C.$ Sketch the graph of the profit function and estimate the number of units that would produce a maximum profit.

(Multiple Choice)

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Question 37

Write the standard form of the equation of the circle whose diameter has endpoints of $( 8 , - 12 )$ and $( 14 , - 4 )$ .

(Multiple Choice)

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Question 38

Find (f?g)(x). $f ( x ) = 4 x ^ { 2 } - 8 x$ $g ( x ) = - 7 - x$

(Multiple Choice)

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Question 39

Given $t ( x ) = 3 x ^ { 2 } + 5,$ find $t ( - 8 ).$

(Multiple Choice)

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Question 40

Showing 21 - 40 of 96

Use the intercept form to find the equation of the line with the given intercepts. The intercept form of the equation of a line with intercepts (a, 0) and (0, b) is $\frac { x } { a } + \frac { y } { b } = 1 , a \neq 0 , b \neq 0$ $x$ -intercept: $( - 4,0 ) \quad y$ -intercept: $( 0,1 )$

Use the graph of $f ( x ) = x ^ { 3 } - 3 x ^ { 2 }$ to write an equation for the function $g$ . $Use the graph of f ( x ) = x ^ { 3 } - 3 x ^ { 2 } to write an equation for the function g .$ $Use the graph of f ( x ) = x ^ { 3 } - 3 x ^ { 2 } to write an equation for the function g .$

Use the graph of the function to find the domain and range of f.

A car was purchased for $42,000. Assuming the car depreciates at a rate of $5040 per year (straight-line depreciation) for the first 5 years, write the value v of the car as a function of the time t (measured in years) for $0 \leq t \leq 5$

Describe the sequence of transformation from $f ( x ) = x ^ { 2 }$ to $g ( x )$ if $g ( x ) = ( x - 6 ) ^ { 2 } - 7$

Find $g \circ f.$ f (x) = x + 4 g (x) = x2

Use a graphing utility to graph the function and approximate (to two decimal places) any relative minimum or relative maximum values. f (x) = x3 - x2 - 2x - 1

Decide whether the function is even, odd, or neither. $g ( x ) = x ^ { 3 } - 5 x$

Consider the graph of $g ( x ) = \sqrt { x }.$ Use your knowledge of rigid and nonrigid transformations to write an equation for the following descriptions. The graph of $g$ is reflected in the x-axis, shifted eight units to the right, and shifted nine unit downward.

Plot the points and find the slope of the line passing through the pair of points. (0, 4), (5, 2)

Use a graphing utility to graph the function, approximate the relative minimum or maximum of the function, and estimate the open intervals on which the function is increasing or decreasing. $f ( x ) = x ^ { 2 } - 4 x + 1$

Find (fg)(x). $f ( x ) = \sqrt { 2 x }$ $g ( x ) = \sqrt { - x + 3 }$

Sketch the graph of the function below. $f ( x ) = \sqrt { - x + 3 }$

Find $x$ such that the distance between the point $( - 2,5 )$ and $( x , 17 )$ is 15.

Use the graph of $f ( x ) = x ^ { 3 }$ to write equations for the functions whose graphs are shown. $Use the graph of f ( x ) = x ^ { 3 } to write equations for the functions whose graphs are shown.$

Write the standard form of the equation of the circle whose diameter has endpoints of $( 8 , - 12 )$ and $( 14 , - 4 )$ .

Find (f?g)(x). $f ( x ) = 4 x ^ { 2 } - 8 x$ $g ( x ) = - 7 - x$

Given $t ( x ) = 3 x ^ { 2 } + 5,$ find $t ( - 8 ).$

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Exam 3: Functions and Graphs

Use the graph of f(x)=x3−3x2f ( x ) = x ^ { 3 } - 3 x ^ { 2 }f(x)=x3−3x2 to write an equation for the function ggg .

Use the graph of the function to find the domain and range of f.

A car was purchased for $42,000. Assuming the car depreciates at a rate of $5040 per year (straight-line depreciation) for the first 5 years, write the value v of the car as a function of the time t (measured in years) for 0≤t≤50 \leq t \leq 50≤t≤5

Describe the sequence of transformation from f(x)=x2f ( x ) = x ^ { 2 }f(x)=x2 to g(x)g ( x )g(x) if g(x)=(x−6)2−7g ( x ) = ( x - 6 ) ^ { 2 } - 7g(x)=(x−6)2−7

Find g∘f.g \circ f.g∘f. f (x) = x + 4 g (x) = x2

Use a graphing utility to graph the function and approximate (to two decimal places) any relative minimum or relative maximum values. f (x) = x3 - x2 - 2x - 1

Decide whether the function is even, odd, or neither. g(x)=x3−5xg ( x ) = x ^ { 3 } - 5 xg(x)=x3−5x

Consider the graph of g(x)=x.g ( x ) = \sqrt { x }.g(x)=x​. Use your knowledge of rigid and nonrigid transformations to write an equation for the following descriptions. The graph of ggg is reflected in the x-axis, shifted eight units to the right, and shifted nine unit downward.

Plot the points and find the slope of the line passing through the pair of points. (0, 4), (5, 2)

An open box is to be made from a square piece of cardboard having dimensions 32 inches by 32 inches by cutting out squares of area x2x ^ { 2 }x2 from each corner as shown in the figure below. Express the volume V of the box as a function of x. 32−2x32 - 2 x32−2x 32−2x32 - 2 x32−2x

Use a graphing utility to graph the function, approximate the relative minimum or maximum of the function, and estimate the open intervals on which the function is increasing or decreasing. f(x)=x2−4x+1f ( x ) = x ^ { 2 } - 4 x + 1f(x)=x2−4x+1

Find (fg)(x). f(x)=2xf ( x ) = \sqrt { 2 x }f(x)=2x​ g(x)=−x+3g ( x ) = \sqrt { - x + 3 }g(x)=−x+3​

Sketch the graph of the function below. f(x)=−x+3f ( x ) = \sqrt { - x + 3 }f(x)=−x+3​

Find xxx such that the distance between the point (−2,5)( - 2,5 )(−2,5) and (x,17)( x , 17 )(x,17) is 15.

Use the graph of f(x)=x3f ( x ) = x ^ { 3 }f(x)=x3 to write equations for the functions whose graphs are shown.

Write the standard form of the equation of the circle whose diameter has endpoints of (8,−12)( 8 , - 12 )(8,−12) and (14,−4)( 14 , - 4 )(14,−4) .

Find (f?g)(x). f(x)=4x2−8xf ( x ) = 4 x ^ { 2 } - 8 xf(x)=4x2−8x g(x)=−7−xg ( x ) = - 7 - xg(x)=−7−x

Given t(x)=3x2+5,t ( x ) = 3 x ^ { 2 } + 5,t(x)=3x2+5, find t(−8).t ( - 8 ).t(−8).

Fundamental Concepts of Algebra

Equations and Inequalities

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants

Limits and Derivatives

Applications of the Derivative

Further Applications of the Derivative

Derivatives of Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions Web

Series and Taylor Polynomials Web

Probability Web

Filters

Use the graph of $f ( x ) = x ^ { 3 } - 3 x ^ { 2 }$ to write an equation for the function $g$ . $Use the graph of f ( x ) = x ^ { 3 } - 3 x ^ { 2 } to write an equation for the function g .$ $Use the graph of f ( x ) = x ^ { 3 } - 3 x ^ { 2 } to write an equation for the function g .$

A car was purchased for $42,000. Assuming the car depreciates at a rate of $5040 per year (straight-line depreciation) for the first 5 years, write the value v of the car as a function of the time t (measured in years) for $0 \leq t \leq 5$

Describe the sequence of transformation from $f ( x ) = x ^ { 2 }$ to $g ( x )$ if $g ( x ) = ( x - 6 ) ^ { 2 } - 7$

Find $g \circ f.$ f (x) = x + 4 g (x) = x2

Decide whether the function is even, odd, or neither. $g ( x ) = x ^ { 3 } - 5 x$

Consider the graph of $g ( x ) = \sqrt { x }.$ Use your knowledge of rigid and nonrigid transformations to write an equation for the following descriptions. The graph of $g$ is reflected in the x-axis, shifted eight units to the right, and shifted nine unit downward.

Use a graphing utility to graph the function, approximate the relative minimum or maximum of the function, and estimate the open intervals on which the function is increasing or decreasing. $f ( x ) = x ^ { 2 } - 4 x + 1$

Find (fg)(x). $f ( x ) = \sqrt { 2 x }$ $g ( x ) = \sqrt { - x + 3 }$

Sketch the graph of the function below. $f ( x ) = \sqrt { - x + 3 }$

Find $x$ such that the distance between the point $( - 2,5 )$ and $( x , 17 )$ is 15.

Use the graph of $f ( x ) = x ^ { 3 }$ to write equations for the functions whose graphs are shown. $Use the graph of f ( x ) = x ^ { 3 } to write equations for the functions whose graphs are shown.$

Write the standard form of the equation of the circle whose diameter has endpoints of $( 8 , - 12 )$ and $( 14 , - 4 )$ .

Find (f?g)(x). $f ( x ) = 4 x ^ { 2 } - 8 x$ $g ( x ) = - 7 - x$

Given $t ( x ) = 3 x ^ { 2 } + 5,$ find $t ( - 8 ).$