Question 1

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

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 2

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

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 3

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

Accepted Answer

The answer of Provide an appropriate response.
-Explain how the graph...

Question 4

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

Accepted Answer

A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \ln ( \mathrm { x } - 1 ) + 3$, domain $= ( - \infty , \infty )$, range $= ( - \infty , \infty )$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \ln ( x - 1 ) + 3$, domain $= ( 3 , \infty )$, range $= ( - \infty , \infty )$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \ln ( x - 3 ) + 1$, domain $= ( 0 , \infty )$, range $= ( 0 , \infty )$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \ln ( \mathrm { x } - 3 ) + 1$, domain $= ( 3 , \infty )$, range $= ( - \infty , \infty )$

Question 5

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

Accepted Answer

A)  $\{ 2 \}$ 
B)  $\{ - 5,2 \}$ 
C)  $\{ - 2,5 \}$ 
D)  $\{ - 2 \}$

Question 6

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

Accepted Answer

A)  {5.015} 
B)  {6.907} 
C)  {10.500} 
D)  {0.907}

Question 7

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

Accepted Answer

A)  domain: $( - 4 , \infty )$; range: $( 0 , \infty )$
 
B)  domain: $( - 4 , \infty )$; range: $( \infty , \infty )$
 
C)  domain: $( 4 , \infty )$; range: $( 0 , \infty )$
 
D)  domain: $( \infty , - 4 )$; range: $( 0 , \infty )$

Question 8

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

Accepted Answer

A) True 
 B)False

Question 9

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

Accepted Answer

A)  3 
B)  1.7 
C)  9 
D)  0

Question 10

Graph the exponential function using transformations where appropriate.
-

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 11

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 $g$.
$$f ( x ) = a ^ { x }$$

Accepted Answer

The answer of Provide an appropriate response.
-The graph of an...

Question 12

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

Accepted Answer

A)  0.3711 
B)  0.3522 
C)  0.8109 
D)  0.3324

Question 13

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

Accepted Answer

A)  The hours taken to travel 29 miles 
B)  The miles traveled in 29 hours 
C)  The miles traveled in 7 hours at 29 miles per hour 
D)  The hours taken to travel 7 miles at 29 miles per hour

Question 14

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

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { \frac { x - 4 } { 6 } }$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \frac { \mathrm { x } } { 6 } } - 4$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \frac { \mathrm { x } + 4 } { 6 } }$ 
D)  not a one-to-one

Question 15

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

Accepted Answer

A)  $\{ ( - 7 , - 7 ) , ( - 9 , - 3 ) , ( - 5 , - 6 ) \}$ 
B)  $\{ ( - 7 , - 9 ) , ( - 7 , - 3 ) , ( - 5 , - 6 ) \}$ 
C)  $\{ ( - 7 , - 7 ) , ( - 6 , - 3 ) , ( - 5 , - 9 ) \}$ 
D)  not one-to-one

Question 16

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

Accepted Answer

A)  2.1875 
B)  4.8921 
C)  0.2044 
D)  55.0000

Question 17

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

Accepted Answer

A)  32.4723 
B)  4.4773 
C)  1.9445 
D)  0.2227

Question 18

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

Accepted Answer

A)  12 yr 
B)  9 yr 
C)  11 yr 
D)  10 yr

Question 19

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

Accepted Answer

A)  $\{ 2 \}$ 
B)  $\{ 5 \}$ 
C)  $\{ 243 \}$ 
D)  $\{ - 2 \}$

Question 20

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.

Accepted Answer

A)  $3.57 
B)  $2.70 
C)  $0.62 
D)  $0.01

Exam 5: Inverse, Exponential, and Logarithmic Functions

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

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. - $2 ( x - 3 ) = 15$

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.

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.

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

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. - $2 ( x - 3 ) = 15$

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.