Exam 2: Functions

Graph the function. - $G ( x ) = \left\{ \begin{array} { l l } | x | + 5 , & x < 0 \\5 , & x \geq 0\end{array} \right.$ $Graph the function. - G ( x ) = \left\{ \begin{array} { l l } | x | + 5 , & x < 0 \\ 5 , & x \geq 0 \end{array} \right.$

(Multiple Choice)

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Question 341

Find the formula for the function. -Express the volume of a sphere as a function of its radius r.

(Multiple Choice)

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Question 342

The problem tells how many units and in what direction the graph of the given equation is to be shifted. Give an equation for the shifted graph. Then sketch the original graph with a dashed line and the shifted graph with a solid line. - $x^{2}+y^{2}=9$ $\text { Jp } 3 \text {, right } 6$ $The problem tells how many units and in what direction the graph of the given equation is to be shifted. Give an equation for the shifted graph. Then sketch the original graph with a dashed line and the shifted graph with a solid line. - x^{2}+y^{2}=9 \text { Jp } 3 \text {, right } 6$

(Multiple Choice)

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Question 343

Use a graph to find an approximate solution to the equation. Round to the nearest thousandth. - $165 ( 1.41 ) ^ { x / 4 } = 330$

(Multiple Choice)

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Question 344

Find the domain and range for the indicated function. - $f ( x ) = \sqrt { x + 7 } , \quad g ( x ) = \sqrt { x - 7 }$ $f \cdot g$

(Multiple Choice)

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Question 345

Solve the problem. -The accompanying figure shows the graph of $y = - x ^ { 2 }$ shifted to a new position. Write the equation for the new graph. $Solve the problem. -The accompanying figure shows the graph of y = - x ^ { 2 } shifted to a new position. Write the equation for the new graph.$

(Multiple Choice)

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Question 346

Determine whether or not the graph is a graph of a function of x. -

(Multiple Choice)

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Question 347

Assume that f is an even function, g is an odd function, and both f and g are defined on the entire real line. State whether the combination of functions (where defined) is even or odd. -g/f

(Multiple Choice)

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Question 348

Is the function graphed below one-to-one? -

(True/False)

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Question 349

Find a formula for the function graphed. -

(Multiple Choice)

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Question 350

Find the exact function value. - $\sin ^ { - 1 } \left( \frac { \sqrt { 3 } } { 2 } \right)$

(Multiple Choice)

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Question 351

Determine an appropriate viewing window for the given function and use it to display its graph. - $f(x)=\sqrt[3]{x-1}$ $Determine an appropriate viewing window for the given function and use it to display its graph. - f(x)=\sqrt[3]{x-1}$

(Multiple Choice)

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Question 352

Solve for t or y, as appropriate. - $\ln y = 4 x + 5$

(Multiple Choice)

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Question 353

Graph the function. Determine the symmetry, if any, of the function. - $y=\sqrt{-x}$ $Graph the function. Determine the symmetry, if any, of the function. - y=\sqrt{-x}$

(Multiple Choice)

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Question 354

Find the inverse of the function. - $f ( x ) = \sqrt { x + 3 } , x \geq - 3$

(Multiple Choice)

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Question 355

Express the given quantity in terms of sin x or cos x. - $\cos ( 4 \pi + x )$

(Multiple Choice)

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Question 356

Determine whether or not the graph is a graph of a function of x. -

(Multiple Choice)

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Question 357

Use the laws of exponents to simplify. Do not use negative exponents in your answer. - $\frac { 81 ^ { 5 } \cdot 3 ^ { - 3 } } { 9 ^ { 5 } }$

(Multiple Choice)

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Question 358

Solve the problem. -The population of a small country increases according to the functio $B = 2,400,000 e ^ { 0.05 } t$ t, where t is measured in years. How many people will the country have after 3 years?

(Multiple Choice)

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Question 359

Express as a single logarithm and, if possible, simplify. - $\frac { 1 } { 2 } \ln \left( 49 t ^ { 16 } \right) - \ln 7$

(Multiple Choice)

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Question 360

Showing 341 - 360 of 413

Graph the function. - $G ( x ) = \left\{ \begin{array} { l l } | x | + 5 , & x < 0 \\5 , & x \geq 0\end{array} \right.$ $Graph the function. - G ( x ) = \left\{ \begin{array} { l l } | x | + 5 , & x < 0 \\ 5 , & x \geq 0 \end{array} \right.$

Find the formula for the function. -Express the volume of a sphere as a function of its radius r.

Use a graph to find an approximate solution to the equation. Round to the nearest thousandth. - $165 ( 1.41 ) ^ { x / 4 } = 330$

Find the domain and range for the indicated function. - $f ( x ) = \sqrt { x + 7 } , \quad g ( x ) = \sqrt { x - 7 }$ $f \cdot g$

Solve the problem. -The accompanying figure shows the graph of $y = - x ^ { 2 }$ shifted to a new position. Write the equation for the new graph. $Solve the problem. -The accompanying figure shows the graph of y = - x ^ { 2 } shifted to a new position. Write the equation for the new graph.$

Determine whether or not the graph is a graph of a function of x. -

Assume that f is an even function, g is an odd function, and both f and g are defined on the entire real line. State whether the combination of functions (where defined) is even or odd. -g/f

Is the function graphed below one-to-one? -

Find a formula for the function graphed. -

Find the exact function value. - $\sin ^ { - 1 } \left( \frac { \sqrt { 3 } } { 2 } \right)$

Determine an appropriate viewing window for the given function and use it to display its graph. - $f(x)=\sqrt[3]{x-1}$ $Determine an appropriate viewing window for the given function and use it to display its graph. - f(x)=\sqrt[3]{x-1}$

Solve for t or y, as appropriate. - $\ln y = 4 x + 5$

Graph the function. Determine the symmetry, if any, of the function. - $y=\sqrt{-x}$ $Graph the function. Determine the symmetry, if any, of the function. - y=\sqrt{-x}$

Find the inverse of the function. - $f ( x ) = \sqrt { x + 3 } , x \geq - 3$

Express the given quantity in terms of sin x or cos x. - $\cos ( 4 \pi + x )$

Determine whether or not the graph is a graph of a function of x. -

Use the laws of exponents to simplify. Do not use negative exponents in your answer. - $\frac { 81 ^ { 5 } \cdot 3 ^ { - 3 } } { 9 ^ { 5 } }$

Solve the problem. -The population of a small country increases according to the functio $B = 2,400,000 e ^ { 0.05 } t$ t, where t is measured in years. How many people will the country have after 3 years?

Express as a single logarithm and, if possible, simplify. - $\frac { 1 } { 2 } \ln \left( 49 t ^ { 16 } \right) - \ln 7$

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)={∣x∣+5,x<05,x≥0G ( x ) = \left\{ \begin{array} { l l } | x | + 5 , & x < 0 \\5 , & x \geq 0\end{array} \right.G(x)={∣x∣+5,5,​x<0x≥0​

Find the formula for the function. -Express the volume of a sphere as a function of its radius r.

Use a graph to find an approximate solution to the equation. Round to the nearest thousandth. - 165(1.41)x/4=330165 ( 1.41 ) ^ { x / 4 } = 330165(1.41)x/4=330

Find the domain and range for the indicated function. - f(x)=x+7,g(x)=x−7f ( x ) = \sqrt { x + 7 } , \quad g ( x ) = \sqrt { x - 7 }f(x)=x+7​,g(x)=x−7​ f⋅gf \cdot gf⋅g

Solve the problem. -The accompanying figure shows the graph of y=−x2y = - x ^ { 2 }y=−x2 shifted to a new position. Write the equation for the new graph.

Determine whether or not the graph is a graph of a function of x. -

Assume that f is an even function, g is an odd function, and both f and g are defined on the entire real line. State whether the combination of functions (where defined) is even or odd. -g/f

Is the function graphed below one-to-one? -

Find a formula for the function graphed. -

Find the exact function value. - sin⁡−1(32)\sin ^ { - 1 } \left( \frac { \sqrt { 3 } } { 2 } \right)sin−1(23​​)

Determine an appropriate viewing window for the given function and use it to display its graph. - f(x)=x−13f(x)=\sqrt[3]{x-1}f(x)=3x−1​

Solve for t or y, as appropriate. - ln⁡y=4x+5\ln y = 4 x + 5lny=4x+5

Graph the function. Determine the symmetry, if any, of the function. - y=−xy=\sqrt{-x}y=−x​

Find the inverse of the function. - f(x)=x+3,x≥−3f ( x ) = \sqrt { x + 3 } , x \geq - 3f(x)=x+3​,x≥−3

Express the given quantity in terms of sin x or cos x. - cos⁡(4π+x)\cos ( 4 \pi + x )cos(4π+x)

Determine whether or not the graph is a graph of a function of x. -

Use the laws of exponents to simplify. Do not use negative exponents in your answer. - 815⋅3−395\frac { 81 ^ { 5 } \cdot 3 ^ { - 3 } } { 9 ^ { 5 } }95815⋅3−3​

Solve the problem. -The population of a small country increases according to the functio B=2,400,000e0.05tB = 2,400,000 e ^ { 0.05 } tB=2,400,000e0.05t t, where t is measured in years. How many people will the country have after 3 years?

Express as a single logarithm and, if possible, simplify. - 12ln⁡(49t16)−ln⁡7\frac { 1 } { 2 } \ln \left( 49 t ^ { 16 } \right) - \ln 721​ln(49t16)−ln7

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. - $G ( x ) = \left\{ \begin{array} { l l } | x | + 5 , & x < 0 \\5 , & x \geq 0\end{array} \right.$ $Graph the function. - G ( x ) = \left\{ \begin{array} { l l } | x | + 5 , & x < 0 \\ 5 , & x \geq 0 \end{array} \right.$

Use a graph to find an approximate solution to the equation. Round to the nearest thousandth. - $165 ( 1.41 ) ^ { x / 4 } = 330$

Find the domain and range for the indicated function. - $f ( x ) = \sqrt { x + 7 } , \quad g ( x ) = \sqrt { x - 7 }$ $f \cdot g$

Solve the problem. -The accompanying figure shows the graph of $y = - x ^ { 2 }$ shifted to a new position. Write the equation for the new graph. $Solve the problem. -The accompanying figure shows the graph of y = - x ^ { 2 } shifted to a new position. Write the equation for the new graph.$

Find the exact function value. - $\sin ^ { - 1 } \left( \frac { \sqrt { 3 } } { 2 } \right)$

Determine an appropriate viewing window for the given function and use it to display its graph. - $f(x)=\sqrt[3]{x-1}$ $Determine an appropriate viewing window for the given function and use it to display its graph. - f(x)=\sqrt[3]{x-1}$

Solve for t or y, as appropriate. - $\ln y = 4 x + 5$

Graph the function. Determine the symmetry, if any, of the function. - $y=\sqrt{-x}$ $Graph the function. Determine the symmetry, if any, of the function. - y=\sqrt{-x}$

Find the inverse of the function. - $f ( x ) = \sqrt { x + 3 } , x \geq - 3$

Express the given quantity in terms of sin x or cos x. - $\cos ( 4 \pi + x )$

Use the laws of exponents to simplify. Do not use negative exponents in your answer. - $\frac { 81 ^ { 5 } \cdot 3 ^ { - 3 } } { 9 ^ { 5 } }$

Solve the problem. -The population of a small country increases according to the functio $B = 2,400,000 e ^ { 0.05 } t$ t, where t is measured in years. How many people will the country have after 3 years?

Express as a single logarithm and, if possible, simplify. - $\frac { 1 } { 2 } \ln \left( 49 t ^ { 16 } \right) - \ln 7$