Exam 1: Functions and Graphs

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Let $\mathrm { f } ( \mathrm { x } )$ compute the time in hours to travel $x$ miles at 32 miles per hour. What does $\mathrm { f } ^ { - 1 } ( \mathrm { x } )$ compute?

(Multiple Choice)

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Question 261

Choose the one alternative that best completes the statement or answers the question. Solve the problem. - $y = ( x - 20 ) ^ { 2 } - 11$

(Multiple Choice)

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Question 262

Choose the one alternative that best completes the statement or answers the question. Solve the problem. - $y = x ^ { 2 } - 13$

(Multiple Choice)

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Question 263

Graph the inverse of the function plotted, on the same set of axes. Use a dashed curve for the inverse. -

(Multiple Choice)

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Question 264

Determine the intervals on which the function is increasing, decreasing, and constant. -

(Multiple Choice)

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Question 265

Identify intervals on which the function is increasing, decreasing, or constant. - $f ( x ) = 0.5 ( x + 4 ) ^ { 2 } - 7$

(Multiple Choice)

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Question 266

Give the equation of the function g whose graph is described. -The graph of $\mathrm { f } ( \mathrm { x } ) = \sqrt { \mathrm { x } }$ is shifted 9 units to the left. Then the graph is shifted 2 units upward.

(Multiple Choice)

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Question 267

Determine whether the formula determines y as a function of x. - $y = - x$

(True/False)

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Question 268

Find the domain of the given function. - $f ( x ) = \frac { \sqrt { x + 2 } } { ( x + 4 ) ( x - 3 ) }$

(Multiple Choice)

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Question 269

Find the range of the function. - $f ( x ) = ( x + 3 ) ^ { 2 } + 7$

(Multiple Choice)

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Question 270

Solve the problem. -Use the graph of $f$ to estimate the local maximum and local minimum.

(Multiple Choice)

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Question 271

Determine the intervals on which the function is increasing, decreasing, and constant. -

(Multiple Choice)

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Question 272

Graph the function on your calculator to determine the domain and range from the graph. - $g ( x ) = 4 \cos x$

(Multiple Choice)

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Question 273

Determine algebraically whether the function is even, odd, or neither even nor odd. - $f ( x ) = 20 \sqrt [ 3 ] { x }$

(Multiple Choice)

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Question 274

Solve the problem. -Use the graph of $f$ to estimate the local maximum and local minimum.

(Multiple Choice)

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Question 275

Sketch the graph of y1 as a solid line or curve. Then sketch the graph of y2 as a dashed line or curve by one or more of these: a vertical and/or horizontal shift of the graph y1, a vertical stretch or shrink of the graph of y1, or a reflection of the graph of y1 across an axis. - $y_{1}=|x| ; y_{2}=|x-5|$ $Sketch the graph of y1 as a solid line or curve. Then sketch the graph of y2 as a dashed line or curve by one or more of these: a vertical and/or horizontal shift of the graph y1, a vertical stretch or shrink of the graph of y1, or a reflection of the graph of y1 across an axis. - y_{1}=|x| ; y_{2}=|x-5|$

(Multiple Choice)

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Question 276

Determine if the function is bounded above, bounded below, bounded on its domain, or unbounded on its domain. - $y = 7 ^ { x + 5 }$

(Multiple Choice)

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Question 277

Solve the equation graphically by converting it to an equivalent equation with 0 on the right-hand side and then finding the x-intercepts. - $| 5 x - 9 | = 3 - | x - 2 |$

(Multiple Choice)

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Question 278

Graph the function on your calculator to determine the domain and range from the graph. - $k ( x ) = e ^ { x } - 3$

(Multiple Choice)

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Question 279

Determine whether the formula determines y as a function of x. - $y ^ { 2 } = ( x - 6 ) ( x + 1 )$

(True/False)

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Question 280

Showing 261 - 280 of 362

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Let $\mathrm { f } ( \mathrm { x } )$ compute the time in hours to travel $x$ miles at 32 miles per hour. What does $\mathrm { f } ^ { - 1 } ( \mathrm { x } )$ compute?

Choose the one alternative that best completes the statement or answers the question. Solve the problem. - $y = ( x - 20 ) ^ { 2 } - 11$

Choose the one alternative that best completes the statement or answers the question. Solve the problem. - $y = x ^ { 2 } - 13$

Graph the inverse of the function plotted, on the same set of axes. Use a dashed curve for the inverse. -

Determine the intervals on which the function is increasing, decreasing, and constant. -

Identify intervals on which the function is increasing, decreasing, or constant. - $f ( x ) = 0.5 ( x + 4 ) ^ { 2 } - 7$

Give the equation of the function g whose graph is described. -The graph of $\mathrm { f } ( \mathrm { x } ) = \sqrt { \mathrm { x } }$ is shifted 9 units to the left. Then the graph is shifted 2 units upward.

Determine whether the formula determines y as a function of x. - $y = - x$

Find the domain of the given function. - $f ( x ) = \frac { \sqrt { x + 2 } } { ( x + 4 ) ( x - 3 ) }$

Find the range of the function. - $f ( x ) = ( x + 3 ) ^ { 2 } + 7$

Solve the problem. -Use the graph of $f$ to estimate the local maximum and local minimum.

Determine the intervals on which the function is increasing, decreasing, and constant. -

Graph the function on your calculator to determine the domain and range from the graph. - $g ( x ) = 4 \cos x$

Determine algebraically whether the function is even, odd, or neither even nor odd. - $f ( x ) = 20 \sqrt [ 3 ] { x }$

Solve the problem. -Use the graph of $f$ to estimate the local maximum and local minimum.

Determine if the function is bounded above, bounded below, bounded on its domain, or unbounded on its domain. - $y = 7 ^ { x + 5 }$

Solve the equation graphically by converting it to an equivalent equation with 0 on the right-hand side and then finding the x-intercepts. - $| 5 x - 9 | = 3 - | x - 2 |$

Graph the function on your calculator to determine the domain and range from the graph. - $k ( x ) = e ^ { x } - 3$

Determine whether the formula determines y as a function of x. - $y ^ { 2 } = ( x - 6 ) ( x + 1 )$

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Exam 1: Functions and Graphs

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Let f(x)\mathrm { f } ( \mathrm { x } )f(x) compute the time in hours to travel xxx miles at 32 miles per hour. What does f−1(x)\mathrm { f } ^ { - 1 } ( \mathrm { x } )f−1(x) compute?

Choose the one alternative that best completes the statement or answers the question. Solve the problem. - y=(x−20)2−11y = ( x - 20 ) ^ { 2 } - 11y=(x−20)2−11

Choose the one alternative that best completes the statement or answers the question. Solve the problem. - y=x2−13y = x ^ { 2 } - 13y=x2−13

Graph the inverse of the function plotted, on the same set of axes. Use a dashed curve for the inverse. -

Determine the intervals on which the function is increasing, decreasing, and constant. -

Identify intervals on which the function is increasing, decreasing, or constant. - f(x)=0.5(x+4)2−7f ( x ) = 0.5 ( x + 4 ) ^ { 2 } - 7f(x)=0.5(x+4)2−7

Give the equation of the function g whose graph is described. -The graph of f(x)=x\mathrm { f } ( \mathrm { x } ) = \sqrt { \mathrm { x } }f(x)=x​ is shifted 9 units to the left. Then the graph is shifted 2 units upward.

Determine whether the formula determines y as a function of x. - y=−xy = - xy=−x

Find the domain of the given function. - f(x)=x+2(x+4)(x−3)f ( x ) = \frac { \sqrt { x + 2 } } { ( x + 4 ) ( x - 3 ) }f(x)=(x+4)(x−3)x+2​​

Find the range of the function. - f(x)=(x+3)2+7f ( x ) = ( x + 3 ) ^ { 2 } + 7f(x)=(x+3)2+7

Solve the problem. -Use the graph of fff to estimate the local maximum and local minimum.

Determine the intervals on which the function is increasing, decreasing, and constant. -

Graph the function on your calculator to determine the domain and range from the graph. - g(x)=4cos⁡xg ( x ) = 4 \cos xg(x)=4cosx

Determine algebraically whether the function is even, odd, or neither even nor odd. - f(x)=20x3f ( x ) = 20 \sqrt [ 3 ] { x }f(x)=203x​

Solve the problem. -Use the graph of fff to estimate the local maximum and local minimum.

Determine if the function is bounded above, bounded below, bounded on its domain, or unbounded on its domain. - y=7x+5y = 7 ^ { x + 5 }y=7x+5

Solve the equation graphically by converting it to an equivalent equation with 0 on the right-hand side and then finding the x-intercepts. - ∣5x−9∣=3−∣x−2∣| 5 x - 9 | = 3 - | x - 2 |∣5x−9∣=3−∣x−2∣

Graph the function on your calculator to determine the domain and range from the graph. - k(x)=ex−3k ( x ) = e ^ { x } - 3k(x)=ex−3

Determine whether the formula determines y as a function of x. - y2=(x−6)(x+1)y ^ { 2 } = ( x - 6 ) ( x + 1 )y2=(x−6)(x+1)

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -Let $\mathrm { f } ( \mathrm { x } )$ compute the time in hours to travel $x$ miles at 32 miles per hour. What does $\mathrm { f } ^ { - 1 } ( \mathrm { x } )$ compute?

Choose the one alternative that best completes the statement or answers the question. Solve the problem. - $y = ( x - 20 ) ^ { 2 } - 11$

Choose the one alternative that best completes the statement or answers the question. Solve the problem. - $y = x ^ { 2 } - 13$

Identify intervals on which the function is increasing, decreasing, or constant. - $f ( x ) = 0.5 ( x + 4 ) ^ { 2 } - 7$

Give the equation of the function g whose graph is described. -The graph of $\mathrm { f } ( \mathrm { x } ) = \sqrt { \mathrm { x } }$ is shifted 9 units to the left. Then the graph is shifted 2 units upward.

Determine whether the formula determines y as a function of x. - $y = - x$

Find the domain of the given function. - $f ( x ) = \frac { \sqrt { x + 2 } } { ( x + 4 ) ( x - 3 ) }$

Find the range of the function. - $f ( x ) = ( x + 3 ) ^ { 2 } + 7$

Solve the problem. -Use the graph of $f$ to estimate the local maximum and local minimum.

Graph the function on your calculator to determine the domain and range from the graph. - $g ( x ) = 4 \cos x$

Determine algebraically whether the function is even, odd, or neither even nor odd. - $f ( x ) = 20 \sqrt [ 3 ] { x }$

Solve the problem. -Use the graph of $f$ to estimate the local maximum and local minimum.

Determine if the function is bounded above, bounded below, bounded on its domain, or unbounded on its domain. - $y = 7 ^ { x + 5 }$

Solve the equation graphically by converting it to an equivalent equation with 0 on the right-hand side and then finding the x-intercepts. - $| 5 x - 9 | = 3 - | x - 2 |$

Graph the function on your calculator to determine the domain and range from the graph. - $k ( x ) = e ^ { x } - 3$

Determine whether the formula determines y as a function of x. - $y ^ { 2 } = ( x - 6 ) ( x + 1 )$