Exam 5: Inverse, Exponential, and Logarithmic Functions

Graph the exponential function using transformations where appropriate. - $f ( x ) = \left( \frac { 1 } { 2 } \right) ^ { x } - 3$ $Graph the exponential function using transformations where appropriate. - f ( x ) = \left( \frac { 1 } { 2 } \right) ^ { x } - 3$

(Multiple Choice)

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Question 101

Use the graph of f to sketch a graph of the inverse of f using a dashed curve. -

(Multiple Choice)

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Question 102

Provide an appropriate response. -Explain how the graph of $y = 3 ^ { x } - 2 - 3 \text { can be obtained from the graph of } y = 3 ^ { x } \text {. }$

(Essay)

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Question 103

Given that $f ( x ) = e ^ { x - 1 } + 3$ , find $f ^ { - 1 } ( x )$ and give the domain and range of $f ^ { - 1 } ( x )$ .

(Multiple Choice)

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Question 104

Solve the equation and express the solution in exact form. - $\log ( x + 3 ) = 1 - \log x$

(Multiple Choice)

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Question 105

Round to the nearest thousandth. - $2 ( x - 3 ) = 15$

(Multiple Choice)

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Question 106

Give the domain and range. - $f ( x ) = \left| \log _ { 1 / 2 } ( x + 4 ) \right|$ $Give the domain and range. - f ( x ) = \left| \log _ { 1 / 2 } ( x + 4 ) \right|$

(Multiple Choice)

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Question 107

Determine whether or not the function is one-to-one. - $f ( x ) = 4 x ^ { 3 } - 8$

(True/False)

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Question 108

The graph of a function f is given. Use the graph to find the indicated value. -

(Multiple Choice)

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Question 109

Graph the exponential function using transformations where appropriate. -

(Multiple Choice)

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Question 110

Provide an appropriate response. -The graph of an exponential function with base a is given. Sketch the graph of $g ( x ) = a x + 2$ . Give the domain anc range of $g$ . $f ( x ) = a ^ { x }$ $Provide an appropriate response. -The graph of an exponential function with base a is given. Sketch the graph of g ( x ) = a x + 2 . Give the domain anc range of g . f ( x ) = a ^ { x }$

(Essay)

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Question 111

Find the value. Give an approximation to four decimal places. -log 2.25

(Multiple Choice)

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Question 112

Let f(x) compute the time in hours to travel x miles at 29 miles per hour. What is the interpretation of $\mathrm { f } ^ { - 1 } ( 7 )$

(Multiple Choice)

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Question 113

If the function is one-to-one, find its inverse. If not, write "not one-to-one." - $f ( x ) = 6 x ^ { 3 } + 4$

(Multiple Choice)

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Question 114

If the function is one-to-one, find its inverse. If not, write "not one-to-one." - $\{ ( - 7 , - 7 ) , ( - 6 , - 7 ) , ( - 5 , - 3 ) , ( - 4 , - 9 ) \}$

(Multiple Choice)

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Question 115

Use the change of base rule to find the logarithm to four decimal places. - $\log _ { 2.8 } 154$

(Multiple Choice)

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Question 116

Find the value. Give an approximation to four decimal places. -ln 88

(Multiple Choice)

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Question 117

How long must $4400 be in a bank at 3% compounded annually to become $5913.23? (Round to the nearest year.)

(Multiple Choice)

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Question 118

Solve the equation. - $3 ( 10 - 2 x ) = 729$

(Multiple Choice)

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Question 119

An economist predicts that the buying power B(x) of a dollar x years from now will decrease according to the form $B ( x ) = 0.51 ^ { x }$ . How much will today's dollar be worth in 7 years? Round the answer to the nearest cent.

(Multiple Choice)

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Question 120

Showing 101 - 120 of 472

Graph the exponential function using transformations where appropriate. - $f ( x ) = \left( \frac { 1 } { 2 } \right) ^ { x } - 3$ $Graph the exponential function using transformations where appropriate. - f ( x ) = \left( \frac { 1 } { 2 } \right) ^ { x } - 3$

Use the graph of f to sketch a graph of the inverse of f using a dashed curve. -

Provide an appropriate response. -Explain how the graph of $y = 3 ^ { x } - 2 - 3 \text { can be obtained from the graph of } y = 3 ^ { x } \text {. }$

Given that $f ( x ) = e ^ { x - 1 } + 3$ , find $f ^ { - 1 } ( x )$ and give the domain and range of $f ^ { - 1 } ( x )$ .

Solve the equation and express the solution in exact form. - $\log ( x + 3 ) = 1 - \log x$

Round to the nearest thousandth. - $2 ( x - 3 ) = 15$

Give the domain and range. - $f ( x ) = \left| \log _ { 1 / 2 } ( x + 4 ) \right|$ $Give the domain and range. - f ( x ) = \left| \log _ { 1 / 2 } ( x + 4 ) \right|$

Determine whether or not the function is one-to-one. - $f ( x ) = 4 x ^ { 3 } - 8$

The graph of a function f is given. Use the graph to find the indicated value. -

Graph the exponential function using transformations where appropriate. -

Find the value. Give an approximation to four decimal places. -log 2.25

Let f(x) compute the time in hours to travel x miles at 29 miles per hour. What is the interpretation of $\mathrm { f } ^ { - 1 } ( 7 )$

If the function is one-to-one, find its inverse. If not, write "not one-to-one." - $f ( x ) = 6 x ^ { 3 } + 4$

If the function is one-to-one, find its inverse. If not, write "not one-to-one." - $\{ ( - 7 , - 7 ) , ( - 6 , - 7 ) , ( - 5 , - 3 ) , ( - 4 , - 9 ) \}$

Use the change of base rule to find the logarithm to four decimal places. - $\log _ { 2.8 } 154$

Find the value. Give an approximation to four decimal places. -ln 88

How long must $4400 be in a bank at 3% compounded annually to become $5913.23? (Round to the nearest year.)

Solve the equation. - $3 ( 10 - 2 x ) = 729$

An economist predicts that the buying power B(x) of a dollar x years from now will decrease according to the form $B ( x ) = 0.51 ^ { x }$ . How much will today's dollar be worth in 7 years? Round the answer to the nearest cent.

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 5: Inverse, Exponential, and Logarithmic Functions

Graph the exponential function using transformations where appropriate. - f(x)=(12)x−3f ( x ) = \left( \frac { 1 } { 2 } \right) ^ { x } - 3f(x)=(21​)x−3

Use the graph of f to sketch a graph of the inverse of f using a dashed curve. -

Provide an appropriate response. -Explain how the graph of y=3x−2−3 can be obtained from the graph of y=3x. y = 3 ^ { x } - 2 - 3 \text { can be obtained from the graph of } y = 3 ^ { x } \text {. }y=3x−2−3 can be obtained from the graph of y=3x.

Given that f(x)=ex−1+3f ( x ) = e ^ { x - 1 } + 3f(x)=ex−1+3 , find f−1(x)f ^ { - 1 } ( x )f−1(x) and give the domain and range of f−1(x)f ^ { - 1 } ( x )f−1(x) .

Solve the equation and express the solution in exact form. - log⁡(x+3)=1−log⁡x\log ( x + 3 ) = 1 - \log xlog(x+3)=1−logx

Round to the nearest thousandth. - 2(x−3)=152 ( x - 3 ) = 152(x−3)=15

Give the domain and range. - f(x)=∣log⁡1/2(x+4)∣f ( x ) = \left| \log _ { 1 / 2 } ( x + 4 ) \right|f(x)=​log1/2​(x+4)​

Determine whether or not the function is one-to-one. - f(x)=4x3−8f ( x ) = 4 x ^ { 3 } - 8f(x)=4x3−8

The graph of a function f is given. Use the graph to find the indicated value. -

Graph the exponential function using transformations where appropriate. -

Provide an appropriate response. -The graph of an exponential function with base a is given. Sketch the graph of g(x)=ax+2g ( x ) = a x + 2g(x)=ax+2 . Give the domain anc range of ggg . f(x)=axf ( x ) = a ^ { x }f(x)=ax

Find the value. Give an approximation to four decimal places. -log 2.25

Let f(x) compute the time in hours to travel x miles at 29 miles per hour. What is the interpretation of f−1(7)\mathrm { f } ^ { - 1 } ( 7 )f−1(7)

If the function is one-to-one, find its inverse. If not, write "not one-to-one." - f(x)=6x3+4f ( x ) = 6 x ^ { 3 } + 4f(x)=6x3+4

If the function is one-to-one, find its inverse. If not, write "not one-to-one." - {(−7,−7),(−6,−7),(−5,−3),(−4,−9)}\{ ( - 7 , - 7 ) , ( - 6 , - 7 ) , ( - 5 , - 3 ) , ( - 4 , - 9 ) \}{(−7,−7),(−6,−7),(−5,−3),(−4,−9)}

Use the change of base rule to find the logarithm to four decimal places. - log⁡2.8154\log _ { 2.8 } 154log2.8​154

Find the value. Give an approximation to four decimal places. -ln 88

How long must $4400 be in a bank at 3% compounded annually to become $5913.23? (Round to the nearest year.)

Solve the equation. - 3(10−2x)=7293 ( 10 - 2 x ) = 7293(10−2x)=729

An economist predicts that the buying power B(x) of a dollar x years from now will decrease according to the form B(x)=0.51xB ( x ) = 0.51 ^ { x }B(x)=0.51x . How much will today's dollar be worth in 7 years? Round the answer to the nearest cent.

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Graph the exponential function using transformations where appropriate. - $f ( x ) = \left( \frac { 1 } { 2 } \right) ^ { x } - 3$ $Graph the exponential function using transformations where appropriate. - f ( x ) = \left( \frac { 1 } { 2 } \right) ^ { x } - 3$

Provide an appropriate response. -Explain how the graph of $y = 3 ^ { x } - 2 - 3 \text { can be obtained from the graph of } y = 3 ^ { x } \text {. }$

Given that $f ( x ) = e ^ { x - 1 } + 3$ , find $f ^ { - 1 } ( x )$ and give the domain and range of $f ^ { - 1 } ( x )$ .

Solve the equation and express the solution in exact form. - $\log ( x + 3 ) = 1 - \log x$

Round to the nearest thousandth. - $2 ( x - 3 ) = 15$

Give the domain and range. - $f ( x ) = \left| \log _ { 1 / 2 } ( x + 4 ) \right|$ $Give the domain and range. - f ( x ) = \left| \log _ { 1 / 2 } ( x + 4 ) \right|$

Determine whether or not the function is one-to-one. - $f ( x ) = 4 x ^ { 3 } - 8$

Let f(x) compute the time in hours to travel x miles at 29 miles per hour. What is the interpretation of $\mathrm { f } ^ { - 1 } ( 7 )$

If the function is one-to-one, find its inverse. If not, write "not one-to-one." - $f ( x ) = 6 x ^ { 3 } + 4$

If the function is one-to-one, find its inverse. If not, write "not one-to-one." - $\{ ( - 7 , - 7 ) , ( - 6 , - 7 ) , ( - 5 , - 3 ) , ( - 4 , - 9 ) \}$

Use the change of base rule to find the logarithm to four decimal places. - $\log _ { 2.8 } 154$

Solve the equation. - $3 ( 10 - 2 x ) = 729$

An economist predicts that the buying power B(x) of a dollar x years from now will decrease according to the form $B ( x ) = 0.51 ^ { x }$ . How much will today's dollar be worth in 7 years? Round the answer to the nearest cent.