Exam 2: Functions

Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - $y = - \frac { 1 } { x ^ { 2 } }$ $Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - y = - \frac { 1 } { x ^ { 2 } }$

(Multiple Choice)

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Question 41

Determine an appropriate viewing window for the given function and use it to display its graph. - $f ( x ) = \frac { x ^ { 3 } } { x ^ { 2 } + 1 }$ $Determine an appropriate viewing window for the given function and use it to display its graph. - f ( x ) = \frac { x ^ { 3 } } { x ^ { 2 } + 1 }$

(Multiple Choice)

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Question 42

Consider the function y Can x be 0? -What real numbers $x$ satisfy the equation $\lfloor x \rfloor = \lceil x \rceil$ ?

(Multiple Choice)

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Question 43

Graph the function. - $y=4-\sqrt{x}$ $Graph the function. - y=4-\sqrt{x}$

(Multiple Choice)

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Question 44

Express the given quantity in terms of sin x or cos x. - $\sin ( 6 \pi + x )$

(Multiple Choice)

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Question 45

Graph the function. - $\mathrm { f } ( \mathrm { x } ) = \mathrm { e } ^ { \mathrm { x } } - 3$ $Graph the function. - \mathrm { f } ( \mathrm { x } ) = \mathrm { e } ^ { \mathrm { x } } - 3$

(Multiple Choice)

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Question 46

Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - $y=\sqrt{-x}$ $Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - y=\sqrt{-x}$

(Multiple Choice)

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Question 47

Solve the problem. -On a circle of radius 18 meters, how long is an arc that subtends a central angle of $\frac { 5 \pi } { 6 }$ radians?

(Multiple Choice)

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Question 48

Find the exact function value. - $\cos ^ { - 1 } ( 1 )$

(Multiple Choice)

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Question 49

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

(Multiple Choice)

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Question 50

Find the exact function value. - $\cot ^ { - 1 } ( - 1 )$

(Multiple Choice)

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Question 51

Simplify the expression. - $\log _ { 6 } \frac { 1 } { 6 }$

(Multiple Choice)

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Question 52

Use the appropriate addition formula to find the exact value of the expression. - $\cos \left( \frac { \pi } { 12 } \right)$

(Multiple Choice)

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Question 53

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. -gf

(Multiple Choice)

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Question 54

Find the exact value of the trigonometric function. Do not use a calculator or tables. - $\sec \left( \frac { \pi } { 6 } \right)$

(Multiple Choice)

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Question 55

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

(Multiple Choice)

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Question 56

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

(Multiple Choice)

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Question 57

Find the function value. - $\cos ^ { 2 } \frac { \pi } { 6 }$

(Multiple Choice)

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Question 58

Graph the function. - $f(x)=4 e^{-x}+5$ $Graph the function. - f(x)=4 e^{-x}+5$

(Multiple Choice)

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Question 59

Express the following logarithm as specified. - $\ln \sqrt { 4.5 }$ in terms of $\ln 3$ and $\ln 2$

(Multiple Choice)

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Question 60

Showing 41 - 60 of 413

Determine an appropriate viewing window for the given function and use it to display its graph. - $f ( x ) = \frac { x ^ { 3 } } { x ^ { 2 } + 1 }$ $Determine an appropriate viewing window for the given function and use it to display its graph. - f ( x ) = \frac { x ^ { 3 } } { x ^ { 2 } + 1 }$

Consider the function y Can x be 0? -What real numbers $x$ satisfy the equation $\lfloor x \rfloor = \lceil x \rceil$ ?

Graph the function. - $y=4-\sqrt{x}$ $Graph the function. - y=4-\sqrt{x}$

Express the given quantity in terms of sin x or cos x. - $\sin ( 6 \pi + x )$

Graph the function. - $\mathrm { f } ( \mathrm { x } ) = \mathrm { e } ^ { \mathrm { x } } - 3$ $Graph the function. - \mathrm { f } ( \mathrm { x } ) = \mathrm { e } ^ { \mathrm { x } } - 3$

Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - $y=\sqrt{-x}$ $Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - y=\sqrt{-x}$

Solve the problem. -On a circle of radius 18 meters, how long is an arc that subtends a central angle of $\frac { 5 \pi } { 6 }$ radians?

Find the exact function value. - $\cos ^ { - 1 } ( 1 )$

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

Find the exact function value. - $\cot ^ { - 1 } ( - 1 )$

Simplify the expression. - $\log _ { 6 } \frac { 1 } { 6 }$

Use the appropriate addition formula to find the exact value of the expression. - $\cos \left( \frac { \pi } { 12 } \right)$

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. -gf

Find the exact value of the trigonometric function. Do not use a calculator or tables. - $\sec \left( \frac { \pi } { 6 } \right)$

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

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

Find the function value. - $\cos ^ { 2 } \frac { \pi } { 6 }$

Graph the function. - $f(x)=4 e^{-x}+5$ $Graph the function. - f(x)=4 e^{-x}+5$

Express the following logarithm as specified. - $\ln \sqrt { 4.5 }$ in terms of $\ln 3$ and $\ln 2$

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

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Exam 2: Functions

Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - y=−1x2y = - \frac { 1 } { x ^ { 2 } }y=−x21​

Determine an appropriate viewing window for the given function and use it to display its graph. - f(x)=x3x2+1f ( x ) = \frac { x ^ { 3 } } { x ^ { 2 } + 1 }f(x)=x2+1x3​

Consider the function y Can x be 0? -What real numbers xxx satisfy the equation ⌊x⌋=⌈x⌉\lfloor x \rfloor = \lceil x \rceil⌊x⌋=⌈x⌉ ?

Graph the function. - y=4−xy=4-\sqrt{x}y=4−x​

Express the given quantity in terms of sin x or cos x. - sin⁡(6π+x)\sin ( 6 \pi + x )sin(6π+x)

Graph the function. - f(x)=ex−3\mathrm { f } ( \mathrm { x } ) = \mathrm { e } ^ { \mathrm { x } } - 3f(x)=ex−3

Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - y=−xy=\sqrt{-x}y=−x​

Solve the problem. -On a circle of radius 18 meters, how long is an arc that subtends a central angle of 5π6\frac { 5 \pi } { 6 }65π​ radians?

Find the exact function value. - cos⁡−1(1)\cos ^ { - 1 } ( 1 )cos−1(1)

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

Find the exact function value. - cot⁡−1(−1)\cot ^ { - 1 } ( - 1 )cot−1(−1)

Simplify the expression. - log⁡616\log _ { 6 } \frac { 1 } { 6 }log6​61​

Use the appropriate addition formula to find the exact value of the expression. - cos⁡(π12)\cos \left( \frac { \pi } { 12 } \right)cos(12π​)

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. -gf

Find the exact value of the trigonometric function. Do not use a calculator or tables. - sec⁡(π6)\sec \left( \frac { \pi } { 6 } \right)sec(6π​)

Find the domain and range of the function. - f(x)=22+xf ( x ) = \frac { 2 } { 2 + \sqrt { x } }f(x)=2+x​2​

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

Find the function value. - cos⁡2π6\cos ^ { 2 } \frac { \pi } { 6 }cos26π​

Graph the function. - f(x)=4e−x+5f(x)=4 e^{-x}+5f(x)=4e−x+5

Express the following logarithm as specified. - ln⁡4.5\ln \sqrt { 4.5 }ln4.5​ in terms of ln⁡3\ln 3ln3 and ln⁡2\ln 2ln2

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

Determine an appropriate viewing window for the given function and use it to display its graph. - $f ( x ) = \frac { x ^ { 3 } } { x ^ { 2 } + 1 }$ $Determine an appropriate viewing window for the given function and use it to display its graph. - f ( x ) = \frac { x ^ { 3 } } { x ^ { 2 } + 1 }$

Consider the function y Can x be 0? -What real numbers $x$ satisfy the equation $\lfloor x \rfloor = \lceil x \rceil$ ?

Graph the function. - $y=4-\sqrt{x}$ $Graph the function. - y=4-\sqrt{x}$

Express the given quantity in terms of sin x or cos x. - $\sin ( 6 \pi + x )$

Graph the function. - $\mathrm { f } ( \mathrm { x } ) = \mathrm { e } ^ { \mathrm { x } } - 3$ $Graph the function. - \mathrm { f } ( \mathrm { x } ) = \mathrm { e } ^ { \mathrm { x } } - 3$

Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - $y=\sqrt{-x}$ $Graph the function. Specify the intervals over which the function is increasing and the intervals where it is decreasing. - y=\sqrt{-x}$

Solve the problem. -On a circle of radius 18 meters, how long is an arc that subtends a central angle of $\frac { 5 \pi } { 6 }$ radians?

Find the exact function value. - $\cos ^ { - 1 } ( 1 )$

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

Find the exact function value. - $\cot ^ { - 1 } ( - 1 )$

Simplify the expression. - $\log _ { 6 } \frac { 1 } { 6 }$

Use the appropriate addition formula to find the exact value of the expression. - $\cos \left( \frac { \pi } { 12 } \right)$

Find the exact value of the trigonometric function. Do not use a calculator or tables. - $\sec \left( \frac { \pi } { 6 } \right)$

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

Find the function value. - $\cos ^ { 2 } \frac { \pi } { 6 }$

Graph the function. - $f(x)=4 e^{-x}+5$ $Graph the function. - f(x)=4 e^{-x}+5$

Express the following logarithm as specified. - $\ln \sqrt { 4.5 }$ in terms of $\ln 3$ and $\ln 2$