Question 1

Write an equivalent expression in exponential form.
-$\log _ { 4 } \sqrt { 410 } = x$

Accepted Answer

A)  $\{ 20 \}$ 
B)  $\{ 5 \}$ 
C)  $\{ 40 \}$ 
D)  $\{ \sqrt { 5 } \}$ 
A)  $\{ 20 \}$ 
B)  $\{ 5 \}$ 
C)  $\{ 40 \}$ 
D)  $\{ \sqrt { 5 } \}$

Question 2

Decide whether the given functions are inverses.
-

Accepted Answer

A) True 
 B)False

Question 3

Find the future value.
-$5789 invested for 9 years at 5% compounded quarterly

Accepted Answer

A)  $9070.48 
B)  $8980.64 
C)  $9053.67 
D)  $9028.86 
A)  $9070.48 
B)  $8980.64 
C)  $9053.67 
D)  $9028.86

Question 4

A population is increasing according to the exponential function defined by $y = 3 e ^ { .04 x }$, where $y$ is in millions and $x$ is the number of years. Which of the following should be done in order to answer the question "How large will the population be in 3 months?"

Accepted Answer

A)  Solve $3 e ^ { .04 x } = 3$. 
B)  Solve $3 e ^ { .04 x } = 1 / 4$. 
C)  Evaluate $\mathrm { y } = 3 \mathrm { e } ^ { .04 ( 1 / 4 ) }$. 
D)  Evaluate $y = 3 e ^ { .04 ( 3 ) }$. 
A)  Solve $3 e ^ { .04 x } = 3$. 
B)  Solve $3 e ^ { .04 x } = 1 / 4$. 
C)  Evaluate $\mathrm { y } = 3 \mathrm { e } ^ { .04 ( 1 / 4 ) }$. 
D)  Evaluate $y = 3 e ^ { .04 ( 3 ) }$.

Question 5

Decide whether the given functions are inverses.
-$$\begin{array} { l } 
f = \{ ( 5,15 ) , ( 6,2 ) , ( 2,24 ) , ( 15,5 ) \} \
g = \{ ( 15,5 ) , ( 2,6 ) , ( 24,2 ) , ( 5,15 ) \}
\end{array}$$

Accepted Answer

A) True 
 B)False

Question 6

Use the definition of inverses to determine whether f and g are inverses.
-$$f ( x ) = 2 x ^ { 2 } + 1 , x \geq 0 ; \quad g ( x ) = \sqrt { \frac { x - 1 } { 2 } } , x \geq 1$$

Accepted Answer

A) True 
 B)False

Question 7

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

Accepted Answer

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

Question 8

If the function is one-to-one, find its inverse. If not, write "not one-to-one."
-$f ( x ) = - 8 x + 1$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = - \frac { 1 } { 8 } x - 1$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = - \frac { 1 } { 8 } \mathrm { x } - \frac { 1 } { 8 }$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = - \frac { 1 } { 8 } \mathrm { x } + \frac { 1 } { 8 }$ 
D)  $f ^ { - 1 } ( x ) = - \frac { 1 } { 8 } x + 1$ 
A)  $f ^ { - 1 } ( x ) = - \frac { 1 } { 8 } x - 1$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = - \frac { 1 } { 8 } \mathrm { x } - \frac { 1 } { 8 }$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = - \frac { 1 } { 8 } \mathrm { x } + \frac { 1 } { 8 }$ 
D)  $f ^ { - 1 } ( x ) = - \frac { 1 } { 8 } x + 1$

Question 9

Find the function value. If the result is irrational, round your answer to the nearest thousandth.
-$$f ( x ) = 2 | x |$$

Accepted Answer

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

Question 10

Graph the exponential function using transformations where appropriate.
-$$f ( x ) = 3 ^ { x } + 4$$

Accepted Answer

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

Question 11

Use the definition of inverses to determine whether f and g are inverses.
-$$f ( x ) = x ^ { 3 } - 3 , \quad g ( x ) = \sqrt [ 3 ] { x + 3 }$$

Accepted Answer

A) True 
 B)False

Question 12

Write in logarithmic form.
-$$\left( \frac { 4 } { 11 } \right) ^ { - 3 } = \frac { 1331 } { 64 }$$

Accepted Answer

A)  $\frac { \log _ { 3 } 4 ^ { - 3 } } { \log _ { 3 } 11 ^ { - 3 } } = \frac { 11 } { 4 }$ 
B)  $\log _ { 3 } \frac { 4 } { 11 } = \frac { 4 ^ { - 3 } } { 11 ^ { - 3 } }$ 
C)  $\log _ { 4 / 11 } \left( \frac { 1331 } { 64 } \right) = - 3$ 
D)  $\log _ { - 3 } \left( \frac { 11 ^ { - 3 } } { 4 ^ { - 3 } } \right) = \frac { 11 } { 4 }$ 
A)  $\frac { \log _ { 3 } 4 ^ { - 3 } } { \log _ { 3 } 11 ^ { - 3 } } = \frac { 11 } { 4 }$ 
B)  $\log _ { 3 } \frac { 4 } { 11 } = \frac { 4 ^ { - 3 } } { 11 ^ { - 3 } }$ 
C)  $\log _ { 4 / 11 } \left( \frac { 1331 } { 64 } \right) = - 3$ 
D)  $\log _ { - 3 } \left( \frac { 11 ^ { - 3 } } { 4 ^ { - 3 } } \right) = \frac { 11 } { 4 }$

Question 13

Write an equivalent expression in exponential form.
-$$\log _ { 4 } x = - 3$$

Accepted Answer

A)  $\{ - 12 \}$ 
B)  $\{ 1 \}$ 
C)  $\left\{ \frac { 1 } { 64 } \right\}$ 
D)  $\left\{ \frac { 1 } { 81 } \right\}$ 
A)  $\{ - 12 \}$ 
B)  $\{ 1 \}$ 
C)  $\left\{ \frac { 1 } { 64 } \right\}$ 
D)  $\left\{ \frac { 1 } { 81 } \right\}$

Question 14

Solve the equation.
-

Accepted Answer

A)  $3 ^ { - x } + 1$ 
B)  $- 3 ^ { x } + 1$ 
C)  $3 ^ { x } + 1$ 
D)  $3 ^ { - x } - 1$ 
A)  $3 ^ { - x } + 1$ 
B)  $- 3 ^ { x } + 1$ 
C)  $3 ^ { x } + 1$ 
D)  $3 ^ { - x } - 1$

Question 15

Find the value. Give an approximation to four decimal places.
-$\log \left( 3.08 \times 10 ^ { 5 } \right)$

Accepted Answer

A)  $5.4886$ 
B)  $- 4.5114$ 
C)  $5.0000$ 
D)  $0.4886$ 
A)  $5.4886$ 
B)  $- 4.5114$ 
C)  $5.0000$ 
D)  $0.4886$

Question 16

Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with $a \neq 1 \text { and } b \neq 1$ .
-$$\frac { 8 } { 9 } \log _ { b } 2 y + \frac { 4 } { 5 } \log b \left( 4 y ^ { 2 } \right)$$

Accepted Answer

A)  $\log _ { b } \left( 8 y ^ { 9 / 10 } \right)$ 
B)  $\log _ { b } \left( 2 ^ { 39 / 20 } y ^ { 63 / 40 } \right)$ 
C)  $\log _ { b } \left( 2 ^ { 112 / 45 } \mathrm { y } ^ { 112 / 45 } \right)$ 
D)  $\log _ { b } \left( 8 \mathrm { y } ^ { 39 / 40 } \right)$ 
A)  $\log _ { b } \left( 8 y ^ { 9 / 10 } \right)$ 
B)  $\log _ { b } \left( 2 ^ { 39 / 20 } y ^ { 63 / 40 } \right)$ 
C)  $\log _ { b } \left( 2 ^ { 112 / 45 } \mathrm { y } ^ { 112 / 45 } \right)$ 
D)  $\log _ { b } \left( 8 \mathrm { y } ^ { 39 / 40 } \right)$

Question 17

Find the present value of the future value.
-$9000, invested for 4 years at 4% compounded quarterly

Accepted Answer

A)  $10,537.21 
B)  $10,553.21 
C)  $7691.39 
D)  $7675.39 
A)  $10,537.21 
B)  $10,553.21 
C)  $7691.39 
D)  $7675.39

Question 18

The graph of a function f is given. Use the graph to find the indicated value.
-$\mathrm{f}^{-1}(2)$

Accepted Answer

A)  $\frac { 2 } { 3 }$ 
B)  $\frac { 3 } { 2 }$ 
C)  2 
D)  6 
A)  $\frac { 2 } { 3 }$ 
B)  $\frac { 3 } { 2 }$ 
C)  2 
D)  6

Question 19

Without using a calculator, explain why $2 ^ { \pi }$ must be greater than 8 but less than 16.

Accepted Answer

Since @#LAT-DLM&; that is @#LAT-DLM& is greater th

Question 20

Decide whether the given functions are inverses.
-$$\begin{array} { l } 
\mathrm { f } = \{ ( 3,6 ) , ( 1,3 ) , ( 0,9 ) \} \
\mathrm { q } = \{ ( 3,1 ) , ( 9,0 ) , ( 6,6 ) \}
\end{array}$$

Accepted Answer

A) True 
 B)False

Write an equivalent expression in exponential form. - $\log _ { 4 } \sqrt { 410 } = x$

Decide whether the given functions are inverses. -

Find the future value. -$5789 invested for 9 years at 5% compounded quarterly

A population is increasing according to the exponential function defined by $y = 3 e ^ { .04 x }$ , where $y$ is in millions and $x$ is the number of years. Which of the following should be done in order to answer the question "How large will the population be in 3 months?"

Decide whether the given functions are inverses. - f=\{(5,15),(6,2),(2,24),(15,5)\} g=\{(15,5),(2,6),(24,2),(5,15)\}

Use the definition of inverses to determine whether f and g are inverses. - $f ( x ) = 2 x ^ { 2 } + 1 , x \geq 0 ; \quad g ( x ) = \sqrt { \frac { x - 1 } { 2 } } , x \geq 1$

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

If the function is one-to-one, find its inverse. If not, write "not one-to-one." - $f ( x ) = - 8 x + 1$

Find the function value. If the result is irrational, round your answer to the nearest thousandth. - $f ( x ) = 2 | x |$

Graph the exponential function using transformations where appropriate. - $f ( x ) = 3 ^ { x } + 4$ $Graph the exponential function using transformations where appropriate. - f ( x ) = 3 ^ { x } + 4$

Use the definition of inverses to determine whether f and g are inverses. - $f ( x ) = x ^ { 3 } - 3 , \quad g ( x ) = \sqrt [ 3 ] { x + 3 }$

Write in logarithmic form. - $\left( \frac { 4 } { 11 } \right) ^ { - 3 } = \frac { 1331 } { 64 }$

Write an equivalent expression in exponential form. - $\log _ { 4 } x = - 3$

Solve the equation. -

Find the value. Give an approximation to four decimal places. - $\log \left( 3.08 \times 10 ^ { 5 } \right)$

Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with $a \neq 1 \text { and } b \neq 1$ . - $\frac { 8 } { 9 } \log _ { b } 2 y + \frac { 4 } { 5 } \log b \left( 4 y ^ { 2 } \right)$

Find the present value of the future value. -$9000, invested for 4 years at 4% compounded quarterly

The graph of a function f is given. Use the graph to find the indicated value. - $\mathrm{f}^{-1}(2)$ $The graph of a function f is given. Use the graph to find the indicated value. - \mathrm{f}^{-1}(2)$

Without using a calculator, explain why $2 ^ { \pi }$ must be greater than 8 but less than 16.

Decide whether the given functions are inverses. - =\{(3,6),(1,3),(0,9)\} =\{(3,1),(9,0),(6,6)\}

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

Write an equivalent expression in exponential form. - log⁡4410=x\log _ { 4 } \sqrt { 410 } = xlog4​410​=x

Decide whether the given functions are inverses. -

Find the future value. -$5789 invested for 9 years at 5% compounded quarterly

A population is increasing according to the exponential function defined by y=3e.04xy = 3 e ^ { .04 x }y=3e.04x , where yyy is in millions and xxx is the number of years. Which of the following should be done in order to answer the question "How large will the population be in 3 months?"

Decide whether the given functions are inverses. - f=\{(5,15),(6,2),(2,24),(15,5)\} g=\{(15,5),(2,6),(24,2),(5,15)\}

Use the definition of inverses to determine whether f and g are inverses. - f(x)=2x2+1,x≥0;g(x)=x−12,x≥1f ( x ) = 2 x ^ { 2 } + 1 , x \geq 0 ; \quad g ( x ) = \sqrt { \frac { x - 1 } { 2 } } , x \geq 1f(x)=2x2+1,x≥0;g(x)=2x−1​​,x≥1

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

If the function is one-to-one, find its inverse. If not, write "not one-to-one." - f(x)=−8x+1f ( x ) = - 8 x + 1f(x)=−8x+1

Find the function value. If the result is irrational, round your answer to the nearest thousandth. - f(x)=2∣x∣f ( x ) = 2 | x |f(x)=2∣x∣

Graph the exponential function using transformations where appropriate. - f(x)=3x+4f ( x ) = 3 ^ { x } + 4f(x)=3x+4

Use the definition of inverses to determine whether f and g are inverses. - f(x)=x3−3,g(x)=x+33f ( x ) = x ^ { 3 } - 3 , \quad g ( x ) = \sqrt [ 3 ] { x + 3 }f(x)=x3−3,g(x)=3x+3​

Write in logarithmic form. - (411)−3=133164\left( \frac { 4 } { 11 } \right) ^ { - 3 } = \frac { 1331 } { 64 }(114​)−3=641331​

Write an equivalent expression in exponential form. - log⁡4x=−3\log _ { 4 } x = - 3log4​x=−3

Solve the equation. -

Find the value. Give an approximation to four decimal places. - log⁡(3.08×105)\log \left( 3.08 \times 10 ^ { 5 } \right)log(3.08×105)

Find the present value of the future value. -$9000, invested for 4 years at 4% compounded quarterly

The graph of a function f is given. Use the graph to find the indicated value. - f−1(2)\mathrm{f}^{-1}(2)f−1(2)

Without using a calculator, explain why 2π2 ^ { \pi }2π must be greater than 8 but less than 16.

Decide whether the given functions are inverses. - =\{(3,6),(1,3),(0,9)\} =\{(3,1),(9,0),(6,6)\}

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

Write an equivalent expression in exponential form. - $\log _ { 4 } \sqrt { 410 } = x$

A population is increasing according to the exponential function defined by $y = 3 e ^ { .04 x }$ , where $y$ is in millions and $x$ is the number of years. Which of the following should be done in order to answer the question "How large will the population be in 3 months?"

Use the definition of inverses to determine whether f and g are inverses. - $f ( x ) = 2 x ^ { 2 } + 1 , x \geq 0 ; \quad g ( x ) = \sqrt { \frac { x - 1 } { 2 } } , x \geq 1$

If the function is one-to-one, find its inverse. If not, write "not one-to-one." - $f ( x ) = - 8 x + 1$

Find the function value. If the result is irrational, round your answer to the nearest thousandth. - $f ( x ) = 2 | x |$

Graph the exponential function using transformations where appropriate. - $f ( x ) = 3 ^ { x } + 4$ $Graph the exponential function using transformations where appropriate. - f ( x ) = 3 ^ { x } + 4$

Use the definition of inverses to determine whether f and g are inverses. - $f ( x ) = x ^ { 3 } - 3 , \quad g ( x ) = \sqrt [ 3 ] { x + 3 }$

Write in logarithmic form. - $\left( \frac { 4 } { 11 } \right) ^ { - 3 } = \frac { 1331 } { 64 }$

Write an equivalent expression in exponential form. - $\log _ { 4 } x = - 3$

Find the value. Give an approximation to four decimal places. - $\log \left( 3.08 \times 10 ^ { 5 } \right)$

The graph of a function f is given. Use the graph to find the indicated value. - $\mathrm{f}^{-1}(2)$ $The graph of a function f is given. Use the graph to find the indicated value. - \mathrm{f}^{-1}(2)$

Without using a calculator, explain why $2 ^ { \pi }$ must be greater than 8 but less than 16.