Exam 1: Functions and Their Graphs

Solve the problem. -The amount of time it takes a swimmer to swim a race is inversely proportional to the average speed of the swimmer. A swimmer finishes a race in 150 seconds with an average speed of 4 feet per second. Find the Average speed of the swimmer if it takes 200 seconds to finish the race.

(Multiple Choice)

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Question 101

Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local minima. If necessary, round answers to two decimal places. - $f ( x ) = x ^ { 3 } - 12 x + 2 ; ( - 5,5 )$

(Multiple Choice)

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Question 102

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - $\left( - 3 , - \frac { 3 } { 2 } \right)$ $The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - \left( - 3 , - \frac { 3 } { 2 } \right)$

(Multiple Choice)

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Question 103

For the graph of the function y = f(x), find the absolute maximum and the absolute minimum, if it exists. -

(Multiple Choice)

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Question 104

Solve the problem. -If the voltage, V, in an electric circuit is held constant, the current, I, is inversely proportional to the resistance, R. If the current is 280 milliamperes when the resistance is 5 ohms, find the current when the resistance is 35 ohms.

(Multiple Choice)

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Question 105

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. -

(Multiple Choice)

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Question 106

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f(x)=\sqrt{x-5}$ $Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - f(x)=\sqrt{x-5}$

(Multiple Choice)

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Question 107

Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local minima. Determine where the function is increasing and where it is decreasing. If necessary, round answers to two decimal places. - $( x ) = x ^ { 3 } - 4 x ^ { 2 } + 6 ; ( - 1,4 )$

(Essay)

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Question 108

Determine algebraically whether the function is even, odd, or neither. - $f ( x ) = \sqrt { x }$

(Multiple Choice)

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Question 109

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. -(-5, -3)

(Multiple Choice)

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Question 110

Match the graph to the function listed whose graph most resembles the one given. -

(Multiple Choice)

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Question 111

Solve the problem. -A farmer has 800 yards of fencing to enclose a rectangular garden. Express the area A of the rectangle as a function of the width x of the rectangle. What is the domain of A?

(Multiple Choice)

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Question 112

Using transformations, sketch the graph of the requested function. -The graph of a function f is illustrated. Use the graph of f as the first step toward graphing the function F(x), where F(x) = f(x + 2) - 1.

(Multiple Choice)

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Question 113

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. -

(Multiple Choice)

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Question 114

Match the graph to the function listed whose graph most resembles the one given. -

(Multiple Choice)

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Question 115

Find the value for the function. - $( - x ) \text { when } f ( x ) = \frac { x } { x ^ { 2 } + 1 }$

(Multiple Choice)

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Question 116

Solve the problem. -While traveling at a constant speed in a car, the centrifugal acceleration passengers feel while the car is turning is inversely proportional to the radius of the turn. If the passengers feel an acceleration of 16 feet per second per Second when the radius of the turn is 60 feet, find the acceleration the passengers feel when the radius of the Turn is 240 feet.

(Multiple Choice)

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Question 117

Solve the problem. -A rectangular sign is being designed so that the length of its base, in feet, is 12 feet less than 4 times the height, h. Express the area of the sign as a function of h.

(Multiple Choice)

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Question 118

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. -

(Multiple Choice)

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Question 119

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function. -The reflection of the graph of y = f(x) across the y-axis

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Question 120

Showing 101 - 120 of 276

Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local minima. If necessary, round answers to two decimal places. - $f ( x ) = x ^ { 3 } - 12 x + 2 ; ( - 5,5 )$

For the graph of the function y = f(x), find the absolute maximum and the absolute minimum, if it exists. -

Solve the problem. -If the voltage, V, in an electric circuit is held constant, the current, I, is inversely proportional to the resistance, R. If the current is 280 milliamperes when the resistance is 5 ohms, find the current when the resistance is 35 ohms.

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. -

Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local minima. Determine where the function is increasing and where it is decreasing. If necessary, round answers to two decimal places. - $( x ) = x ^ { 3 } - 4 x ^ { 2 } + 6 ; ( - 1,4 )$

Determine algebraically whether the function is even, odd, or neither. - $f ( x ) = \sqrt { x }$

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. -(-5, -3)

Match the graph to the function listed whose graph most resembles the one given. -

Solve the problem. -A farmer has 800 yards of fencing to enclose a rectangular garden. Express the area A of the rectangle as a function of the width x of the rectangle. What is the domain of A?

Using transformations, sketch the graph of the requested function. -The graph of a function f is illustrated. Use the graph of f as the first step toward graphing the function F(x), where F(x) = f(x + 2) - 1.

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. -

Match the graph to the function listed whose graph most resembles the one given. -

Find the value for the function. - $( - x ) \text { when } f ( x ) = \frac { x } { x ^ { 2 } + 1 }$

Solve the problem. -A rectangular sign is being designed so that the length of its base, in feet, is 12 feet less than 4 times the height, h. Express the area of the sign as a function of h.

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. -

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function. -The reflection of the graph of y = f(x) across the y-axis

Linear and Quadratic Functions

Polynomial and Rational Functions

Conics

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

Filters

Exam 1: Functions and Their Graphs

Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local minima. If necessary, round answers to two decimal places. - f(x)=x3−12x+2;(−5,5)f ( x ) = x ^ { 3 } - 12 x + 2 ; ( - 5,5 )f(x)=x3−12x+2;(−5,5)

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - (−3,−32)\left( - 3 , - \frac { 3 } { 2 } \right)(−3,−23​)

For the graph of the function y = f(x), find the absolute maximum and the absolute minimum, if it exists. -

Solve the problem. -If the voltage, V, in an electric circuit is held constant, the current, I, is inversely proportional to the resistance, R. If the current is 280 milliamperes when the resistance is 5 ohms, find the current when the resistance is 35 ohms.

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. -

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - f(x)=x−5f(x)=\sqrt{x-5}f(x)=x−5​

Determine algebraically whether the function is even, odd, or neither. - f(x)=xf ( x ) = \sqrt { x }f(x)=x​

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. -(-5, -3)

Match the graph to the function listed whose graph most resembles the one given. -

Solve the problem. -A farmer has 800 yards of fencing to enclose a rectangular garden. Express the area A of the rectangle as a function of the width x of the rectangle. What is the domain of A?

Using transformations, sketch the graph of the requested function. -The graph of a function f is illustrated. Use the graph of f as the first step toward graphing the function F(x), where F(x) = f(x + 2) - 1.

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. -

Match the graph to the function listed whose graph most resembles the one given. -

Find the value for the function. - (−x) when f(x)=xx2+1( - x ) \text { when } f ( x ) = \frac { x } { x ^ { 2 } + 1 }(−x) when f(x)=x2+1x​

Solve the problem. -A rectangular sign is being designed so that the length of its base, in feet, is 12 feet less than 4 times the height, h. Express the area of the sign as a function of h.

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. -

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function. -The reflection of the graph of y = f(x) across the y-axis

Linear and Quadratic Functions

Polynomial and Rational Functions

Conics

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

Filters

Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local minima. If necessary, round answers to two decimal places. - $f ( x ) = x ^ { 3 } - 12 x + 2 ; ( - 5,5 )$

Determine algebraically whether the function is even, odd, or neither. - $f ( x ) = \sqrt { x }$

Find the value for the function. - $( - x ) \text { when } f ( x ) = \frac { x } { x ^ { 2 } + 1 }$