Question 1

Give a definition for the following term: Logarithmic function .

Accepted Answer

The answer of Give a definition for the following term:...

Question 2

Graph the exponential function using transformations where appropriate.
-

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 3

Give the domain and range.
-$f(x)=\log 1 / 4(1-x)$

Accepted Answer

A)  domain: $( - 1 , \infty )$; range: $( \infty , \infty )$
  
B)  domain: $( \infty , 1 )$; range: $( \infty , \infty )$
  
C)  domain: $( - 1 , \infty )$; range: $( \infty , \infty )$
  
D)  domain: $( \infty , 1 )$; range: $( \infty , \infty )$
  
A)  domain: $( - 1 , \infty )$; range: $( \infty , \infty )$
  
B)  domain: $( \infty , 1 )$; range: $( \infty , \infty )$
  
C)  domain: $( - 1 , \infty )$; range: $( \infty , \infty )$
  
D)  domain: $( \infty , 1 )$; range: $( \infty , \infty )$

Question 4

Solve for the indicated variable.
-$A = \frac { t s } { 1 - ( 1 + z ) ^ { - B } }$, for B

Accepted Answer

A)  $B = \frac { \ln A - \ln ( A - t s ) } { \ln ( 1 + z ) }$ 
B)  $B = \ln \frac { t } { ( A - A s ) ( 1 + z ) }$ 
C)  $B = \frac { \ln t } { \ln [ ( A - A s ) ( 1 - z ) ] }$ 
D)  $B = \ln \frac { A } { ( A - t s ) ( 1 + z ) }$ 
A)  $B = \frac { \ln A - \ln ( A - t s ) } { \ln ( 1 + z ) }$ 
B)  $B = \ln \frac { t } { ( A - A s ) ( 1 + z ) }$ 
C)  $B = \frac { \ln t } { \ln [ ( A - A s ) ( 1 - z ) ] }$ 
D)  $B = \ln \frac { A } { ( A - t s ) ( 1 + z ) }$

Question 5

Let f(x) compute the cost of a rental car after x days of use at $24 per day. What does $\mathrm { f } ^ { - 1 } ( \mathrm { x } )$ compute?

Accepted Answer

A)  The cost of rental for 24 days 
B)  The number of days rented for x dollars 
C)  The number of days rented for 24 dollars 
D)  The cost of rental for x days 
A)  The cost of rental for 24 days 
B)  The number of days rented for x dollars 
C)  The number of days rented for 24 dollars 
D)  The cost of rental for x days

Question 6

Find the value. Give an approximation to four decimal places.
-ln $137 - \ln 14$

Accepted Answer

A)  $7.5590$ 
B)  $2.2809$ 
C)  $- 1.0638$ 
D)  $1.8643$ 
A)  $7.5590$ 
B)  $2.2809$ 
C)  $- 1.0638$ 
D)  $1.8643$

Question 7

Determine whether the statement is true or false.
-The function f $f ( x ) = m x + b$ b is a one-to-one function for all values of m and b.

Accepted Answer

A) True 
 B)False

Question 8

Find the function value. If the result is irrational, round your answer to the nearest thousandth.
-Let $g ( x ) = \left( \frac { 1 } { 3 } \right) ^ { x }$. Find $g ( 5.5 )$.

Accepted Answer

A)  $0.002$ 
B)  $0.004$ 
C)  $420.888$ 
D)  $- 16.5$ 
A)  $0.002$ 
B)  $0.004$ 
C)  $420.888$ 
D)  $- 16.5$

Question 9

Use the change of base rule to find the logarithm to four decimal places.
-$\log _ { 8.2 } 3.7$

Accepted Answer

A)  0.6218 
B)  0.4512 
C)  0.5682 
D)  1.6083 
A)  0.6218 
B)  0.4512 
C)  0.5682 
D)  1.6083

Question 10

Determine whether or not the function is one-to-one.
-

Accepted Answer

A) True 
 B)False

Question 11

Determine the function value.
-Suppose $f ( x ) = \log _ { a } x$ and $f ( 4 ) = 2$. Find $f \left( \frac { 1 } { 16 } \right)$

Accepted Answer

A)  $- 4$ 
B)  $\frac { 1 } { 2 }$ 
C)  $- 2$ 
D)  4 
A)  $- 4$ 
B)  $\frac { 1 } { 2 }$ 
C)  $- 2$ 
D)  4

Question 12

Round to the nearest thousandth.
-$$e ^ { 8 x } e ^ { 6 x } = e ^ { 7 }$$

Accepted Answer

A)  $\{ 2.490 \}$ 
B)  $\{ 0.500 \}$ 
C)  $\{ - 1.490 \}$ 
D)  $\{ 0.642 \}$ 
A)  $\{ 2.490 \}$ 
B)  $\{ 0.500 \}$ 
C)  $\{ - 1.490 \}$ 
D)  $\{ 0.642 \}$

Question 13

Find the value. Give an approximation to four decimal places.
-log 0.00227

Accepted Answer

A)  $- 2.6635$ 
B)  $- 6.0880$ 
C)  $- 2.6440$ 
D)  $- 2.6253$ 
A)  $- 2.6635$ 
B)  $- 6.0880$ 
C)  $- 2.6440$ 
D)  $- 2.6253$

Question 14

Provide an appropriate response.
-The graph of an exponential function with base a is given. Is $a > 1$ or is $0 < a < 1$ ? Explain how you arrived at yoi answer. Give the domain and range of $f$.
$$f ( x ) = a ^ { x }$$

Accepted Answer

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

Question 15

If the function is one-to-one, find its inverse. If not, write "not one-to-one."
-$$f ( x ) = ( x - 6 ) ^ { 2 }$$

Accepted Answer

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

Question 16

Use a graphing calculator to graph the function using the given viewing window. Use the graph to decide if the function
is one-to-one. If the function is one-to-one, give the equation of the inverse function.
-$$f ( x ) = \frac { - x } { x + 2 } ; [ - 8,8 ] \text { by } [ - 8,8 ]$$

Accepted Answer

A)  one-to-one; $f ^ { - 1 } ( x ) = \frac { - 2 x } { x + 1 }$ 
B)  one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 2 \mathrm { x } } { \mathrm { x } + 1 }$ 
C)  not one-to-one 
D)  one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { - \mathrm { x } } { \mathrm { x } + 2 }$ 
A)  one-to-one; $f ^ { - 1 } ( x ) = \frac { - 2 x } { x + 1 }$ 
B)  one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 2 \mathrm { x } } { \mathrm { x } + 1 }$ 
C)  not one-to-one 
D)  one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { - \mathrm { x } } { \mathrm { x } + 2 }$

Question 17

Solve the equation.
-

Accepted Answer

A)  $2 ^ { x + 2 } - 4$ 
B)  $2 ^ { x - 2 } - 4$ 
C)  $2 ^ { x + 2 } + 4$ 
D)  $2 ^ { x - 2 } + 4$ 
A)  $2 ^ { x + 2 } - 4$ 
B)  $2 ^ { x - 2 } - 4$ 
C)  $2 ^ { x + 2 } + 4$ 
D)  $2 ^ { x - 2 } + 4$

Question 18

Solve the equation and express the solution in exact form.
-$$\log _ { 2 } \sqrt { 2 x ^ { 2 } } = \frac { 11 } { 2 }$$

Accepted Answer

A)  $\{ - 16,16 \}$ 
B)  $\{ 32 \}$ 
C)  $\{ - 32,32 \}$ 
D)  $\{ - 1024,1024 \}$ 
A)  $\{ - 16,16 \}$ 
B)  $\{ 32 \}$ 
C)  $\{ - 32,32 \}$ 
D)  $\{ - 1024,1024 \}$

Question 19

Find the domain and range of the inverse of the given function.
-$$f ( x ) = 5 x - 1$$

Accepted Answer

A)  Domain: $[ 5 , \infty )$, range: $( - \infty , - 1 ]$ 
B)  Domain: all real numbers, range: $( - \infty , - 1 ]$ 
C)  Domain and range: all real numbers 
D)  Domain: $( - \infty , - 1 ]$; range: all real numbers 
A)  Domain: $[ 5 , \infty )$, range: $( - \infty , - 1 ]$ 
B)  Domain: all real numbers, range: $( - \infty , - 1 ]$ 
C)  Domain and range: all real numbers 
D)  Domain: $( - \infty , - 1 ]$; range: all real numbers

Question 20

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers.
-$\log _ { b } \left( \frac { m ^ { 7 } p ^ { 5 } } { n ^ { 3 } b ^ { 2 } } \right)$

Accepted Answer

A)  $\log _ { b } m ^ { 7 } + \log _ { b } p ^ { 5 } + \log _ { b } n ^ { 3 } - \log _ { b } b ^ { 2 }$ 
B)  $7 \log _ { b } m + 5 \log _ { b } p - 3 \log _ { b } n + 2$ 
C)  $7 \log _ { b } m + 5 \log _ { b } p - 3 \log _ { b } n - 2$ 
D)  $m ^ { 7 } p ^ { 5 } - n ^ { 3 } b ^ { 2 }$ 
A)  $\log _ { b } m ^ { 7 } + \log _ { b } p ^ { 5 } + \log _ { b } n ^ { 3 } - \log _ { b } b ^ { 2 }$ 
B)  $7 \log _ { b } m + 5 \log _ { b } p - 3 \log _ { b } n + 2$ 
C)  $7 \log _ { b } m + 5 \log _ { b } p - 3 \log _ { b } n - 2$ 
D)  $m ^ { 7 } p ^ { 5 } - n ^ { 3 } b ^ { 2 }$

Give a definition for the following term: Logarithmic function .

Graph the exponential function using transformations where appropriate. -

Give the domain and range. - $f(x)=\log 1 / 4(1-x)$ $Give the domain and range. - f(x)=\log 1 / 4(1-x)$

Solve for the indicated variable. - $A = \frac { t s } { 1 - ( 1 + z ) ^ { - B } }$ , for B

Let f(x) compute the cost of a rental car after x days of use at $24 per day. What does $\mathrm { f } ^ { - 1 } ( \mathrm { x } )$ compute?

Find the value. Give an approximation to four decimal places. -ln $137 - \ln 14$

Determine whether the statement is true or false. -The function f $f ( x ) = m x + b$ b is a one-to-one function for all values of m and b.

Find the function value. If the result is irrational, round your answer to the nearest thousandth. -Let $g ( x ) = \left( \frac { 1 } { 3 } \right) ^ { x }$ . Find $g ( 5.5 )$ .

Use the change of base rule to find the logarithm to four decimal places. - $\log _ { 8.2 } 3.7$

Determine whether or not the function is one-to-one. -

Determine the function value. -Suppose $f ( x ) = \log _ { a } x$ and $f ( 4 ) = 2$ . Find $f \left( \frac { 1 } { 16 } \right)$

Round to the nearest thousandth. - $e ^ { 8 x } e ^ { 6 x } = e ^ { 7 }$

Find the value. Give an approximation to four decimal places. -log 0.00227

If the function is one-to-one, find its inverse. If not, write "not one-to-one." - $f ( x ) = ( x - 6 ) ^ { 2 }$

Use a graphing calculator to graph the function using the given viewing window. Use the graph to decide if the function is one-to-one. If the function is one-to-one, give the equation of the inverse function. - $f ( x ) = \frac { - x } { x + 2 } ; [ - 8,8 ] \text { by } [ - 8,8 ]$

Solve the equation. -

Solve the equation and express the solution in exact form. - $\log _ { 2 } \sqrt { 2 x ^ { 2 } } = \frac { 11 } { 2 }$

Find the domain and range of the inverse of the given function. - $f ( x ) = 5 x - 1$

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers. - $\log _ { b } \left( \frac { m ^ { 7 } p ^ { 5 } } { n ^ { 3 } b ^ { 2 } } \right)$

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

Give a definition for the following term: Logarithmic function .

Graph the exponential function using transformations where appropriate. -

Give the domain and range. - f(x)=log⁡1/4(1−x)f(x)=\log 1 / 4(1-x)f(x)=log1/4(1−x)

Solve for the indicated variable. - A=ts1−(1+z)−BA = \frac { t s } { 1 - ( 1 + z ) ^ { - B } }A=1−(1+z)−Bts​ , for B

Let f(x) compute the cost of a rental car after x days of use at $24 per day. What does f−1(x)\mathrm { f } ^ { - 1 } ( \mathrm { x } )f−1(x) compute?

Find the value. Give an approximation to four decimal places. -ln 137−ln⁡14137 - \ln 14137−ln14

Determine whether the statement is true or false. -The function f f(x)=mx+bf ( x ) = m x + bf(x)=mx+b b is a one-to-one function for all values of m and b.

Find the function value. If the result is irrational, round your answer to the nearest thousandth. -Let g(x)=(13)xg ( x ) = \left( \frac { 1 } { 3 } \right) ^ { x }g(x)=(31​)x . Find g(5.5)g ( 5.5 )g(5.5) .

Use the change of base rule to find the logarithm to four decimal places. - log⁡8.23.7\log _ { 8.2 } 3.7log8.2​3.7

Determine whether or not the function is one-to-one. -

Determine the function value. -Suppose f(x)=log⁡axf ( x ) = \log _ { a } xf(x)=loga​x and f(4)=2f ( 4 ) = 2f(4)=2 . Find f(116)f \left( \frac { 1 } { 16 } \right)f(161​)

Round to the nearest thousandth. - e8xe6x=e7e ^ { 8 x } e ^ { 6 x } = e ^ { 7 }e8xe6x=e7

Find the value. Give an approximation to four decimal places. -log 0.00227

Provide an appropriate response. -The graph of an exponential function with base a is given. Is a>1a > 1a>1 or is 0<a<10 < a < 10<a<1 ? Explain how you arrived at yoi answer. Give the domain and range of fff . f(x)=axf ( x ) = a ^ { x }f(x)=ax

If the function is one-to-one, find its inverse. If not, write "not one-to-one." - f(x)=(x−6)2f ( x ) = ( x - 6 ) ^ { 2 }f(x)=(x−6)2

Solve the equation. -

Solve the equation and express the solution in exact form. - log⁡22x2=112\log _ { 2 } \sqrt { 2 x ^ { 2 } } = \frac { 11 } { 2 }log2​2x2​=211​

Find the domain and range of the inverse of the given function. - f(x)=5x−1f ( x ) = 5 x - 1f(x)=5x−1

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers. - log⁡b(m7p5n3b2)\log _ { b } \left( \frac { m ^ { 7 } p ^ { 5 } } { n ^ { 3 } b ^ { 2 } } \right)logb​(n3b2m7p5​)

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

Give the domain and range. - $f(x)=\log 1 / 4(1-x)$ $Give the domain and range. - f(x)=\log 1 / 4(1-x)$

Solve for the indicated variable. - $A = \frac { t s } { 1 - ( 1 + z ) ^ { - B } }$ , for B

Let f(x) compute the cost of a rental car after x days of use at $24 per day. What does $\mathrm { f } ^ { - 1 } ( \mathrm { x } )$ compute?

Find the value. Give an approximation to four decimal places. -ln $137 - \ln 14$

Determine whether the statement is true or false. -The function f $f ( x ) = m x + b$ b is a one-to-one function for all values of m and b.

Find the function value. If the result is irrational, round your answer to the nearest thousandth. -Let $g ( x ) = \left( \frac { 1 } { 3 } \right) ^ { x }$ . Find $g ( 5.5 )$ .

Use the change of base rule to find the logarithm to four decimal places. - $\log _ { 8.2 } 3.7$

Determine the function value. -Suppose $f ( x ) = \log _ { a } x$ and $f ( 4 ) = 2$ . Find $f \left( \frac { 1 } { 16 } \right)$

Round to the nearest thousandth. - $e ^ { 8 x } e ^ { 6 x } = e ^ { 7 }$

If the function is one-to-one, find its inverse. If not, write "not one-to-one." - $f ( x ) = ( x - 6 ) ^ { 2 }$

Solve the equation and express the solution in exact form. - $\log _ { 2 } \sqrt { 2 x ^ { 2 } } = \frac { 11 } { 2 }$

Find the domain and range of the inverse of the given function. - $f ( x ) = 5 x - 1$

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers. - $\log _ { b } \left( \frac { m ^ { 7 } p ^ { 5 } } { n ^ { 3 } b ^ { 2 } } \right)$