Exam 2: Functions

Graph the function. - $g ( x ) = \left\{ \begin{array} { l l } \frac { 1 } { x + 1 } , & x < - 1 \\x , & x \geq - 1\end{array} \right.$ $Graph the function. - g ( x ) = \left\{ \begin{array} { l l } \frac { 1 } { x + 1 } , & x < - 1 \\ x , & x \geq - 1 \end{array} \right.$

(Multiple Choice)

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Question 241

Simplify the expression. - $e ^ { - \ln x ^ { 10 } }$

(Multiple Choice)

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Question 242

Find the domain and range of the function. - $g ( z ) = \sqrt { 25 - z ^ { 2 } }$

(Multiple Choice)

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Question 243

State the domain and range of the function. - $f ( x ) = e ^ { x } + 2$

(Multiple Choice)

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Question 244

Determine from its graph if the function is one-to-one. - $f ( x ) = \left\{ \begin{array} { l l } 8 x + 6 , & x < 0 \\2 x ^ { 2 } - 5 , & x \geq 0\end{array} \right.$

(True/False)

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Question 245

Solve the problem. -Let $g ( x ) = \sqrt { x }$ . Find a function $y = f ( x )$ so that $( f \circ g ) ( x ) = | x |$ .

(Multiple Choice)

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Question 246

Express the given quantity in terms of sin x or cos x. - $\sin \left( \frac { 7 \pi } { 2 } + x \right)$

(Multiple Choice)

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Question 247

Express the given quantity in terms of sin x or cos x. - $\sin ( 5 \pi + x )$

(Multiple Choice)

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Question 248

Solve the problem. -Use the formu $\mathrm { P } = \mathrm { Ie } ^ { \mathrm { kt } }$ where P is the resulting population, I is the initial population, and t is measured in hours. A bacterial culture has an initial population of 10,000. If its population declines to 3000 in 6 hours, what Will it be at the end of 8 hours?

(Multiple Choice)

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Question 249

Find the domain and range of the inverse of the given function. - $f ( x ) = ( 8 x - 1 ) ^ { 3 }$

(Multiple Choice)

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Question 250

Graph the function. Determine the symmetry, if any, of the function. - $y = \frac { 1 } { x ^ { 3 } }$ $Graph the function. Determine the symmetry, if any, of the function. - y = \frac { 1 } { x ^ { 3 } }$

(Multiple Choice)

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Question 251

Graph the function. - $f ( x ) = \left\{ \begin{array} { l l } - 5 - x , & x < 1 \\1 , & x \geq 1\end{array} \right.$ $Graph the function. - f ( x ) = \left\{ \begin{array} { l l } - 5 - x , & x < 1 \\ 1 , & x \geq 1 \end{array} \right.$

(Multiple Choice)

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Question 252

State the domain and range of the function. - $f ( x ) = 2 ^ { x } + 5$

(Multiple Choice)

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Question 253

Express as a single logarithm and, if possible, simplify. - $\ln ( 32 x + 16 ) - 2 \ln 4$

(Multiple Choice)

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Question 254

Graph the function. - $\text { Graph five periods of the function } \mathrm { f } ( \mathrm { x } ) = \tan 4 \mathrm { x } \text {. }$ $Graph the function. - \text { Graph five periods of the function } \mathrm { f } ( \mathrm { x } ) = \tan 4 \mathrm { x } \text {. }$

(Multiple Choice)

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Question 255

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

(Multiple Choice)

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Question 256

Use a graph to find an approximate solution to the equation. Round to the nearest thousandth. - $5 ( x - 1 ) = 9$

(Multiple Choice)

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Question 257

Find the formula for the function. -Express the area of a circle as a function of its radius r.

(Multiple Choice)

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Question 258

Determine an appropriate viewing window for the given function and use it to display its graph. - $f ( x ) = \frac { \sin 3 x } { x }$ $Determine an appropriate viewing window for the given function and use it to display its graph. - f ( x ) = \frac { \sin 3 x } { x }$

(Multiple Choice)

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Question 259

Use a graph to find an approximate solution to the equation. Round to the nearest thousandth. - $4 e ^ { 2 x + 6 } = 20$

(Multiple Choice)

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Question 260

Showing 241 - 260 of 413

Graph the function. - $g ( x ) = \left\{ \begin{array} { l l } \frac { 1 } { x + 1 } , & x < - 1 \\x , & x \geq - 1\end{array} \right.$ $Graph the function. - g ( x ) = \left\{ \begin{array} { l l } \frac { 1 } { x + 1 } , & x < - 1 \\ x , & x \geq - 1 \end{array} \right.$

Simplify the expression. - $e ^ { - \ln x ^ { 10 } }$

Find the domain and range of the function. - $g ( z ) = \sqrt { 25 - z ^ { 2 } }$

State the domain and range of the function. - $f ( x ) = e ^ { x } + 2$

Determine from its graph if the function is one-to-one. - $f ( x ) = \left\{ \begin{array} { l l } 8 x + 6 , & x < 0 \\2 x ^ { 2 } - 5 , & x \geq 0\end{array} \right.$

Solve the problem. -Let $g ( x ) = \sqrt { x }$ . Find a function $y = f ( x )$ so that $( f \circ g ) ( x ) = | x |$ .

Express the given quantity in terms of sin x or cos x. - $\sin \left( \frac { 7 \pi } { 2 } + x \right)$

Express the given quantity in terms of sin x or cos x. - $\sin ( 5 \pi + x )$

Find the domain and range of the inverse of the given function. - $f ( x ) = ( 8 x - 1 ) ^ { 3 }$

Graph the function. Determine the symmetry, if any, of the function. - $y = \frac { 1 } { x ^ { 3 } }$ $Graph the function. Determine the symmetry, if any, of the function. - y = \frac { 1 } { x ^ { 3 } }$

Graph the function. - $f ( x ) = \left\{ \begin{array} { l l } - 5 - x , & x < 1 \\1 , & x \geq 1\end{array} \right.$ $Graph the function. - f ( x ) = \left\{ \begin{array} { l l } - 5 - x , & x < 1 \\ 1 , & x \geq 1 \end{array} \right.$

State the domain and range of the function. - $f ( x ) = 2 ^ { x } + 5$

Express as a single logarithm and, if possible, simplify. - $\ln ( 32 x + 16 ) - 2 \ln 4$

Graph the function. - $\text { Graph five periods of the function } \mathrm { f } ( \mathrm { x } ) = \tan 4 \mathrm { x } \text {. }$ $Graph the function. - \text { Graph five periods of the function } \mathrm { f } ( \mathrm { x } ) = \tan 4 \mathrm { x } \text {. }$

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

Use a graph to find an approximate solution to the equation. Round to the nearest thousandth. - $5 ( x - 1 ) = 9$

Find the formula for the function. -Express the area of a circle as a function of its radius r.

Determine an appropriate viewing window for the given function and use it to display its graph. - $f ( x ) = \frac { \sin 3 x } { x }$ $Determine an appropriate viewing window for the given function and use it to display its graph. - f ( x ) = \frac { \sin 3 x } { x }$

Use a graph to find an approximate solution to the equation. Round to the nearest thousandth. - $4 e ^ { 2 x + 6 } = 20$

Limits and Continuity

Derivatives

Applications of Derivatives

Integrals

Applications of Definite Integrals

Integrals and Transcendental Functions

Techniques of Integration

First-Order Differential Equations

Infinite Sequences and Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions and Motion in Space

Partial Derivatives

Multiple Integrals

Integrals and Vector Fields

Filters

Exam 2: Functions

Graph the function. - g(x)={1x+1,x<−1x,x≥−1g ( x ) = \left\{ \begin{array} { l l } \frac { 1 } { x + 1 } , & x < - 1 \\x , & x \geq - 1\end{array} \right.g(x)={x+11​,x,​x<−1x≥−1​

Simplify the expression. - e−ln⁡x10e ^ { - \ln x ^ { 10 } }e−lnx10

Find the domain and range of the function. - g(z)=25−z2g ( z ) = \sqrt { 25 - z ^ { 2 } }g(z)=25−z2​

State the domain and range of the function. - f(x)=ex+2f ( x ) = e ^ { x } + 2f(x)=ex+2

Determine from its graph if the function is one-to-one. - f(x)={8x+6,x<02x2−5,x≥0f ( x ) = \left\{ \begin{array} { l l } 8 x + 6 , & x < 0 \\2 x ^ { 2 } - 5 , & x \geq 0\end{array} \right.f(x)={8x+6,2x2−5,​x<0x≥0​

Solve the problem. -Let g(x)=xg ( x ) = \sqrt { x }g(x)=x​ . Find a function y=f(x)y = f ( x )y=f(x) so that (f∘g)(x)=∣x∣( f \circ g ) ( x ) = | x |(f∘g)(x)=∣x∣ .

Express the given quantity in terms of sin x or cos x. - sin⁡(7π2+x)\sin \left( \frac { 7 \pi } { 2 } + x \right)sin(27π​+x)

Express the given quantity in terms of sin x or cos x. - sin⁡(5π+x)\sin ( 5 \pi + x )sin(5π+x)

Find the domain and range of the inverse of the given function. - f(x)=(8x−1)3f ( x ) = ( 8 x - 1 ) ^ { 3 }f(x)=(8x−1)3

Graph the function. Determine the symmetry, if any, of the function. - y=1x3y = \frac { 1 } { x ^ { 3 } }y=x31​

Graph the function. - f(x)={−5−x,x<11,x≥1f ( x ) = \left\{ \begin{array} { l l } - 5 - x , & x < 1 \\1 , & x \geq 1\end{array} \right.f(x)={−5−x,1,​x<1x≥1​

State the domain and range of the function. - f(x)=2x+5f ( x ) = 2 ^ { x } + 5f(x)=2x+5

Express as a single logarithm and, if possible, simplify. - ln⁡(32x+16)−2ln⁡4\ln ( 32 x + 16 ) - 2 \ln 4ln(32x+16)−2ln4

Graph the function. - Graph five periods of the function f(x)=tan⁡4x. \text { Graph five periods of the function } \mathrm { f } ( \mathrm { x } ) = \tan 4 \mathrm { x } \text {. } Graph five periods of the function f(x)=tan4x.

Find the inverse of the function. - f(x)=x3−7f ( x ) = x ^ { 3 } - 7f(x)=x3−7

Use a graph to find an approximate solution to the equation. Round to the nearest thousandth. - 5(x−1)=95 ( x - 1 ) = 95(x−1)=9

Find the formula for the function. -Express the area of a circle as a function of its radius r.

Determine an appropriate viewing window for the given function and use it to display its graph. - f(x)=sin⁡3xxf ( x ) = \frac { \sin 3 x } { x }f(x)=xsin3x​

Use a graph to find an approximate solution to the equation. Round to the nearest thousandth. - 4e2x+6=204 e ^ { 2 x + 6 } = 204e2x+6=20

Limits and Continuity

Derivatives

Applications of Derivatives

Integrals

Applications of Definite Integrals

Integrals and Transcendental Functions

Techniques of Integration

First-Order Differential Equations

Infinite Sequences and Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions and Motion in Space

Partial Derivatives

Multiple Integrals

Integrals and Vector Fields

Filters

Graph the function. - $g ( x ) = \left\{ \begin{array} { l l } \frac { 1 } { x + 1 } , & x < - 1 \\x , & x \geq - 1\end{array} \right.$ $Graph the function. - g ( x ) = \left\{ \begin{array} { l l } \frac { 1 } { x + 1 } , & x < - 1 \\ x , & x \geq - 1 \end{array} \right.$

Simplify the expression. - $e ^ { - \ln x ^ { 10 } }$

Find the domain and range of the function. - $g ( z ) = \sqrt { 25 - z ^ { 2 } }$

State the domain and range of the function. - $f ( x ) = e ^ { x } + 2$

Determine from its graph if the function is one-to-one. - $f ( x ) = \left\{ \begin{array} { l l } 8 x + 6 , & x < 0 \\2 x ^ { 2 } - 5 , & x \geq 0\end{array} \right.$

Solve the problem. -Let $g ( x ) = \sqrt { x }$ . Find a function $y = f ( x )$ so that $( f \circ g ) ( x ) = | x |$ .

Express the given quantity in terms of sin x or cos x. - $\sin \left( \frac { 7 \pi } { 2 } + x \right)$

Express the given quantity in terms of sin x or cos x. - $\sin ( 5 \pi + x )$

Find the domain and range of the inverse of the given function. - $f ( x ) = ( 8 x - 1 ) ^ { 3 }$

Graph the function. Determine the symmetry, if any, of the function. - $y = \frac { 1 } { x ^ { 3 } }$ $Graph the function. Determine the symmetry, if any, of the function. - y = \frac { 1 } { x ^ { 3 } }$

Graph the function. - $f ( x ) = \left\{ \begin{array} { l l } - 5 - x , & x < 1 \\1 , & x \geq 1\end{array} \right.$ $Graph the function. - f ( x ) = \left\{ \begin{array} { l l } - 5 - x , & x < 1 \\ 1 , & x \geq 1 \end{array} \right.$

State the domain and range of the function. - $f ( x ) = 2 ^ { x } + 5$

Express as a single logarithm and, if possible, simplify. - $\ln ( 32 x + 16 ) - 2 \ln 4$

Graph the function. - $\text { Graph five periods of the function } \mathrm { f } ( \mathrm { x } ) = \tan 4 \mathrm { x } \text {. }$ $Graph the function. - \text { Graph five periods of the function } \mathrm { f } ( \mathrm { x } ) = \tan 4 \mathrm { x } \text {. }$

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

Use a graph to find an approximate solution to the equation. Round to the nearest thousandth. - $5 ( x - 1 ) = 9$

Determine an appropriate viewing window for the given function and use it to display its graph. - $f ( x ) = \frac { \sin 3 x } { x }$ $Determine an appropriate viewing window for the given function and use it to display its graph. - f ( x ) = \frac { \sin 3 x } { x }$

Use a graph to find an approximate solution to the equation. Round to the nearest thousandth. - $4 e ^ { 2 x + 6 } = 20$