Exam 1: Functions and Their Graphs

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f(x)=-x^{3}$ $Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - f(x)=-x^{3}$

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Question 281

Solve the problem. -If a rock falls from a height of 70 meters on Earth, the height $\mathrm { H }$ (in meters) after $\mathrm { x }$ seconds is approximately $\mathrm { H } ( \mathrm { x } ) = 70 - 4.9 \mathrm { x } ^ { 2 }$ When does the rock strike the ground? Round to the nearest hundredth, if necessary.

(Multiple Choice)

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Question 282

Graph the function. - $f ( x ) = \sqrt [ 3 ] { x }$ $Graph the function. - f ( x ) = \sqrt [ 3 ] { x }$

(Multiple Choice)

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Question 283

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - $(1, x)$

(Multiple Choice)

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Question 284

Graph the function. - $f(x)=\left\{\begin{array}{ll}-x+2 & x<0 \\\sqrt{x}+3 & x \geq 0\end{array}\right.$ $Graph the function. - f(x)=\left\{\begin{array}{ll} -x+2 & x<0 \\ \sqrt{x}+3 & x \geq 0 \end{array}\right.$

(Multiple Choice)

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Question 285

Choose the one alternative that best completes the statement or answers the question. -A farmer's silo is the shape of a cylinder with a hemisphere as the roof. If the height of the silo is 66 feet and the radius of the hemisphere is $r$ feet, express the volume of the silo as a function of $r$ .

(Multiple Choice)

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Question 286

Find the domain of the function. - $f ( x ) = \sqrt { 24 - x }$

(Multiple Choice)

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Question 287

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = 9 x - 5 ; g ( x ) = 4 x - 8$ Find $\mathrm { f } - \mathrm { g }$ .

(Multiple Choice)

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Question 288

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - $( 0,1 )$

(Multiple Choice)

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Question 289

Find the domain of the function. - $\frac { x } { \sqrt { x - 2 } }$

(Multiple Choice)

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Question 290

Choose the one alternative that best completes the statement or answers the question. -A rocket is shot straight up in the air from the ground at a rate of 80 feet per second. The rocket is tracked by a range finder that is 431 feet from the launch pad. Let $d$ represent the distance from the rocket to the range finder and t represent the time, in seconds, since "blastoff". Express $\mathrm { d }$ as a function of $t$

(Multiple Choice)

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Question 291

Find the value for the function. -Find $f ( x + h )$ when $f ( x ) = 2 x ^ { 2 } + 3 x - 3$

(Multiple Choice)

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Question 292

Choose the one alternative that best completes the statement or answers the question. Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f(x)=\sqrt{x-6}+3$ $Choose the one alternative that best completes the statement or answers the question. Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - f(x)=\sqrt{x-6}+3$

(Multiple Choice)

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Question 293

Match the function with the graph that best describes the situation. -The amount of rainfall as a function of time, if the rain fell more and more softly.

(Multiple Choice)

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Question 294

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

(Multiple Choice)

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Question 295

Answer the question about the given function. - $\text { Given the function } f ( x ) = - 2 x ^ { 2 } - 4 x + 3 \text {, is the point } ( - 2 , - 1 ) \text { on the graph of } f \text { ? }$

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Question 296

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

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Question 297

Showing 281 - 297 of 297

Graph the function. - $f ( x ) = \sqrt [ 3 ] { x }$ $Graph the function. - f ( x ) = \sqrt [ 3 ] { x }$

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - $(1, x)$

Graph the function. - $f(x)=\left\{\begin{array}{ll}-x+2 & x<0 \\\sqrt{x}+3 & x \geq 0\end{array}\right.$ $Graph the function. - f(x)=\left\{\begin{array}{ll} -x+2 & x<0 \\ \sqrt{x}+3 & x \geq 0 \end{array}\right.$

Choose the one alternative that best completes the statement or answers the question. -A farmer's silo is the shape of a cylinder with a hemisphere as the roof. If the height of the silo is 66 feet and the radius of the hemisphere is $r$ feet, express the volume of the silo as a function of $r$ .

Find the domain of the function. - $f ( x ) = \sqrt { 24 - x }$

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = 9 x - 5 ; g ( x ) = 4 x - 8$ Find $\mathrm { f } - \mathrm { g }$ .

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - $( 0,1 )$

Find the domain of the function. - $\frac { x } { \sqrt { x - 2 } }$

Find the value for the function. -Find $f ( x + h )$ when $f ( x ) = 2 x ^ { 2 } + 3 x - 3$

Match the function with the graph that best describes the situation. -The amount of rainfall as a function of time, if the rain fell more and more softly.

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

Answer the question about the given function. - $\text { Given the function } f ( x ) = - 2 x ^ { 2 } - 4 x + 3 \text {, is the point } ( - 2 , - 1 ) \text { on the graph of } f \text { ? }$

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Exam 1: Functions and Their Graphs

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)=−x3f(x)=-x^{3}f(x)=−x3

Graph the function. - f(x)=x3f ( x ) = \sqrt [ 3 ] { x }f(x)=3x​

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - (1,x)(1, x)(1,x)

Graph the function. - f(x)={−x+2x<0x+3x≥0f(x)=\left\{\begin{array}{ll}-x+2 & x<0 \\\sqrt{x}+3 & x \geq 0\end{array}\right.f(x)={−x+2x​+3​x<0x≥0​

Choose the one alternative that best completes the statement or answers the question. -A farmer's silo is the shape of a cylinder with a hemisphere as the roof. If the height of the silo is 66 feet and the radius of the hemisphere is rrr feet, express the volume of the silo as a function of rrr .

Find the domain of the function. - f(x)=24−xf ( x ) = \sqrt { 24 - x }f(x)=24−x​

For the given functions f and g, find the requested function and state its domain. - f(x)=9x−5;g(x)=4x−8f ( x ) = 9 x - 5 ; g ( x ) = 4 x - 8f(x)=9x−5;g(x)=4x−8 Find f−g\mathrm { f } - \mathrm { g }f−g .

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - (0,1)( 0,1 )(0,1)

Find the domain of the function. - xx−2\frac { x } { \sqrt { x - 2 } }x−2​x​

Find the value for the function. -Find f(x+h)f ( x + h )f(x+h) when f(x)=2x2+3x−3f ( x ) = 2 x ^ { 2 } + 3 x - 3f(x)=2x2+3x−3

Choose the one alternative that best completes the statement or answers the question. 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−6+3f(x)=\sqrt{x-6}+3f(x)=x−6​+3

Match the function with the graph that best describes the situation. -The amount of rainfall as a function of time, if the rain fell more and more softly.

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∣f(x)=-|x|f(x)=−∣x∣

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)=5xf(x)=5 \sqrt{x}f(x)=5x​

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Graph the function. - $f ( x ) = \sqrt [ 3 ] { x }$ $Graph the function. - f ( x ) = \sqrt [ 3 ] { x }$

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - $(1, x)$

Graph the function. - $f(x)=\left\{\begin{array}{ll}-x+2 & x<0 \\\sqrt{x}+3 & x \geq 0\end{array}\right.$ $Graph the function. - f(x)=\left\{\begin{array}{ll} -x+2 & x<0 \\ \sqrt{x}+3 & x \geq 0 \end{array}\right.$

Choose the one alternative that best completes the statement or answers the question. -A farmer's silo is the shape of a cylinder with a hemisphere as the roof. If the height of the silo is 66 feet and the radius of the hemisphere is $r$ feet, express the volume of the silo as a function of $r$ .

Find the domain of the function. - $f ( x ) = \sqrt { 24 - x }$

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = 9 x - 5 ; g ( x ) = 4 x - 8$ Find $\mathrm { f } - \mathrm { g }$ .

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - $( 0,1 )$

Find the domain of the function. - $\frac { x } { \sqrt { x - 2 } }$

Find the value for the function. -Find $f ( x + h )$ when $f ( x ) = 2 x ^ { 2 } + 3 x - 3$

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