Question 1

Find the present value of the future value.
-$6000, invested for 4 years at 3% compounded monthly

Accepted Answer

A)  $6751.97 
B)  $6763.97 
C)  $5334.32 
D)  $5322.32 
A)  $6751.97 
B)  $6763.97 
C)  $5334.32 
D)  $5322.32

Question 2

Decide whether the given functions are inverses.
-$\begin{array}{l|l}
x & f(x) \
\hline 3 & 14 \
4 & 16 \
5 & 18 \
6 & 20 \
7 & 22
\end{array}$

$\begin{array}{c|c}
x & g(x) \
\hline 14 & 3 \
16 & 4 \
18 & 5 \
20 & 6 \
22 & 7
\end{array}$

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 3

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.
-$$f ( x ) = x ^ { 4 } - 6 x ^ { 2 } + 5 ; [ - 3,3 ] \text { by } [ - 40,40 ]$$

Accepted Answer

A)  one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 4 ] { \mathrm { x-5 } }$ 
B)  one-to-one; $f ^ { - 1 } ( x ) = \sqrt [ 4 ] { x - 5 } + 6 x ^ { 2 }$ 
C)  one-to-one; $f ^ { - 1 } ( x ) = \sqrt [ 4 ] { 6 x ^ { 2 } - 5 }$ 
D)  not one-to-one 
A)  one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 4 ] { \mathrm { x-5 } }$ 
B)  one-to-one; $f ^ { - 1 } ( x ) = \sqrt [ 4 ] { x - 5 } + 6 x ^ { 2 }$ 
C)  one-to-one; $f ^ { - 1 } ( x ) = \sqrt [ 4 ] { 6 x ^ { 2 } - 5 }$ 
D)  not one-to-one

Question 4

Solve the problem.
-$$p ( t ) = 9270 e ^ { 0.004 t }$$ , where t is the number of years. According to this formula, how many years will it take the population to double
Its year 0 value? Round to the nearest tenth of a year.

Accepted Answer

A)  173.3 yr 
B)  346.6 yr 
C)  130.0 yr 
D)  86.7 yr 
A)  173.3 yr 
B)  346.6 yr 
C)  130.0 yr 
D)  86.7 yr

Question 5

Round your answer to the nearest tenth, when appropriate. Use the formula $\mathrm { pH } = - \log \left[ \mathrm { H } _ { 3 } \mathrm { O } ^ { + } \right] , \text {as }$ needed.
-Find $\left[ \mathrm { H } _ { 3 } \mathrm { O } ^ { + } \right]$if the $\mathrm { pH } = 9.4$.

Accepted Answer

A)  $2.5 \times 10 ^ { - 9 }$ 
B)  $4.0 \times 10 ^ { - 9 }$ 
C)  $4.0 \times 10 - 10$ 
D)  $2.5 \times 10 ^ { - 10 }$ 
A)  $2.5 \times 10 ^ { - 9 }$ 
B)  $4.0 \times 10 ^ { - 9 }$ 
C)  $4.0 \times 10 - 10$ 
D)  $2.5 \times 10 ^ { - 10 }$

Question 6

For the function as defined that is one-to-one, graph f and $$\mathbf { f } ^ { - 1 }$$ on the same axes.
-$f(x)=3 x$

Accepted Answer

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

Question 7

Find the value. Give an approximation to four decimal places.
-$$\ln \sqrt [ 5 ] { \mathrm { e } }$$

Accepted Answer

A)  4 
B)  $\frac { 1 } { 5 }$ 
C)  5 
D)  6 
A)  4 
B)  $\frac { 1 } { 5 }$ 
C)  5 
D)  6

Question 8

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

Accepted Answer

A)  No 
B)  Yes 
A)  No 
B)  Yes

Question 9

Solve the equation.
-$$4 ^ { x - 3 } = 32 ^ { 4 x }$$

Accepted Answer

A)  $\left\{ - \frac { 1 } { 3 } \right\}$ 
B)  $\left\{ - \frac { 1 } { 6 } \right\}$ 
C)  $\{ - 1 \}$ 
D)  $\left\{ - \frac { 6 } { 7 } \right\}$ 
A)  $\left\{ - \frac { 1 } { 3 } \right\}$ 
B)  $\left\{ - \frac { 1 } { 6 } \right\}$ 
C)  $\{ - 1 \}$ 
D)  $\left\{ - \frac { 6 } { 7 } \right\}$

Question 10

Find the domain and range of the inverse of the given function.
-$$f ( x ) = x ^ { 3 } + 5$$

Accepted Answer

A)  Domain: all real numbers; range: $[ 5 , \infty )$ 
B)  Domain: $[ 0 , \infty )$; range: $[ 0 , \infty )$ 
C)  Domain: $[ 5 , \infty )$; range: all real numbers 
D)  Domain and range: all real numbers 
A)  Domain: all real numbers; range: $[ 5 , \infty )$ 
B)  Domain: $[ 0 , \infty )$; range: $[ 0 , \infty )$ 
C)  Domain: $[ 5 , \infty )$; range: all real numbers 
D)  Domain and range: all real numbers

Question 11

Graph the function.
-$f(x)=5|x|$

Accepted Answer

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

Question 12

Determine whether the statement is true or false.
-If a function f has an inverse function and the domain of f is all real numbers, then the domain of 
f-1 must also be all real numbers.

Accepted Answer

A) True 
 B)False

Question 13

Choose the one alternative that best completes the statement or answers the question.
-Suppose $f ( x ) = 32.6 + 1.3 \log ( x + 1 )$ models salinity of ocean water to depths of 1000 meters at a certain latitude. $x$ is the depth in meters and $f ( x )$ is in grams of salt per kilogram of seawater. Approximate the depth (to the nearest tenth of a meter) where the salinity equals 35 .

Accepted Answer

A)  $- 1.0 \mathrm {~g} / \mathrm { kg }$ 
B)  $69.2 \mathrm {~g} / \mathrm { kg }$ 
C)  $- 0.9 \mathrm {~g} / \mathrm { kg }$ 
D)  $71.2 \mathrm {~g} / \mathrm { kg }$ 
A)  $- 1.0 \mathrm {~g} / \mathrm { kg }$ 
B)  $69.2 \mathrm {~g} / \mathrm { kg }$ 
C)  $- 0.9 \mathrm {~g} / \mathrm { kg }$ 
D)  $71.2 \mathrm {~g} / \mathrm { kg }$

Question 14

Choose the one alternative that best completes the statement or answers the question.
-The amount of particulate matter left in solution during a filtering process is given by the equation $P = 700 ( 2 ) ^ { - 0.4 n }$, where $n$ is the number of filtering steps. Find the amounts left for $n = 0$ and $n = 5$. (Round to the nearest whole number.)

Accepted Answer

A)  700,2800 
B)  700,22 
C)  700,175 
D)  1400,175 
A)  700,2800 
B)  700,22 
C)  700,175 
D)  1400,175

Question 15

Solve the problem.
-What is the rate on an investment that doubles $9537 in 20 years? Assume interest is compounded quarterly.

Accepted Answer

A)  4.4% 
B)  3.5% 
C)  1.7% 
D)  2.6% 
A)  4.4% 
B)  3.5% 
C)  1.7% 
D)  2.6%

Question 16

For the function as defined that is one-to-one, graph f and $$\mathbf { f } ^ { - 1 }$$ on the same axes.
-$f(x)=x^{3}+4$

Accepted Answer

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

Question 17

Find the future value.
-$4013 invested for 9 years at 4.1% compounded quarterly

Accepted Answer

A)  $5761.37 
B)  $5782.34 
C)  $5800.30 
D)  $5793.06 
A)  $5761.37 
B)  $5782.34 
C)  $5800.30 
D)  $5793.06

Question 18

Decide whether the pair of functions graphed are inverses.
-

Accepted Answer

A)  No 
B)  Yes 
A)  No 
B)  Yes

Question 19

If the function is one-to-one, find its inverse. If not, write "not one-to-one."
-$$f ( x ) = \sqrt [ 3 ] { x - 2 }$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = ( x - 2 ) ^ { 3 }$ 
B)  $f ^ { - 1 } ( x ) = x ^ { 3 } + 2$ 
C)  $f ^ { - 1 } ( x ) = ( x + 2 ) ^ { 3 }$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } } - 2$ 
A)  $f ^ { - 1 } ( x ) = ( x - 2 ) ^ { 3 }$ 
B)  $f ^ { - 1 } ( x ) = x ^ { 3 } + 2$ 
C)  $f ^ { - 1 } ( x ) = ( x + 2 ) ^ { 3 }$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } } - 2$

Question 20

Write the word or phrase that best completes each statement or answers the question.
-Given $f ( x ) = \ln x$, evaluate the following.
(a) $f \left( e ^ { 6 } \right)$
(b) $f \left( e ^ { \ln 3 } \right)$
(c) $f \left( e ^ { 5 \ln 3 } \right)$

Accepted Answer

The answer of Write the word or phrase that best...

Find the present value of the future value. -$6000, invested for 4 years at 3% compounded monthly

Decide whether the given functions are inverses. - x f(x) 3 14 4 16 5 18 6 20 7 22 x g(x) 14 3 16 4 18 5 20 6 22 7

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. - $f ( x ) = x ^ { 4 } - 6 x ^ { 2 } + 5 ; [ - 3,3 ] \text { by } [ - 40,40 ]$

Solve the problem. - $p ( t ) = 9270 e ^ { 0.004 t }$ , where t is the number of years. According to this formula, how many years will it take the population to double Its year 0 value? Round to the nearest tenth of a year.

Round your answer to the nearest tenth, when appropriate. Use the formula $\mathrm { pH } = - \log \left[ \mathrm { H } _ { 3 } \mathrm { O } ^ { + } \right] , \text {as }$ needed. -Find $\left[ \mathrm { H } _ { 3 } \mathrm { O } ^ { + } \right]$ if the $\mathrm { pH } = 9.4$ .

For the function as defined that is one-to-one, graph f and $\mathbf { f } ^ { - 1 }$ on the same axes. - $f(x)=3 x$ $For the function as defined that is one-to-one, graph f and \mathbf { f } ^ { - 1 } on the same axes. - f(x)=3 x$

Find the value. Give an approximation to four decimal places. - $\ln \sqrt [ 5 ] { \mathrm { e } }$

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

Solve the equation. - $4 ^ { x - 3 } = 32 ^ { 4 x }$

Find the domain and range of the inverse of the given function. - $f ( x ) = x ^ { 3 } + 5$

Graph the function. - $f(x)=5|x|$

Determine whether the statement is true or false. -If a function f has an inverse function and the domain of f is all real numbers, then the domain of f-1 must also be all real numbers.

Solve the problem. -What is the rate on an investment that doubles $9537 in 20 years? Assume interest is compounded quarterly.

For the function as defined that is one-to-one, graph f and $\mathbf { f } ^ { - 1 }$ on the same axes. - $f(x)=x^{3}+4$ $For the function as defined that is one-to-one, graph f and \mathbf { f } ^ { - 1 } on the same axes. - f(x)=x^{3}+4$

Find the future value. -$4013 invested for 9 years at 4.1% compounded quarterly

Decide whether the pair of functions graphed are inverses. -

If the function is one-to-one, find its inverse. If not, write "not one-to-one." - $f ( x ) = \sqrt [ 3 ] { x - 2 }$

Write the word or phrase that best completes each statement or answers the question. -Given $f ( x ) = \ln x$ , evaluate the following. (a) $f \left( e ^ { 6 } \right)$ (b) $f \left( e ^ { \ln 3 } \right)$ (c) $f \left( e ^ { 5 \ln 3 } \right)$

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Exam 5: Inverse, Exponential, and Logarithmic Functions

Find the present value of the future value. -$6000, invested for 4 years at 3% compounded monthly

Decide whether the given functions are inverses. - x f(x) 3 14 4 16 5 18 6 20 7 22 x g(x) 14 3 16 4 18 5 20 6 22 7

Solve the problem. - p(t)=9270e0.004tp ( t ) = 9270 e ^ { 0.004 t }p(t)=9270e0.004t , where t is the number of years. According to this formula, how many years will it take the population to double Its year 0 value? Round to the nearest tenth of a year.

For the function as defined that is one-to-one, graph f and f−1\mathbf { f } ^ { - 1 }f−1 on the same axes. - f(x)=3xf(x)=3 xf(x)=3x

Find the value. Give an approximation to four decimal places. - ln⁡e5\ln \sqrt [ 5 ] { \mathrm { e } }ln5e​

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

Solve the equation. - 4x−3=324x4 ^ { x - 3 } = 32 ^ { 4 x }4x−3=324x

Find the domain and range of the inverse of the given function. - f(x)=x3+5f ( x ) = x ^ { 3 } + 5f(x)=x3+5

Graph the function. - f(x)=5∣x∣f(x)=5|x|f(x)=5∣x∣

Determine whether the statement is true or false. -If a function f has an inverse function and the domain of f is all real numbers, then the domain of f-1 must also be all real numbers.

Solve the problem. -What is the rate on an investment that doubles $9537 in 20 years? Assume interest is compounded quarterly.

For the function as defined that is one-to-one, graph f and f−1\mathbf { f } ^ { - 1 }f−1 on the same axes. - f(x)=x3+4f(x)=x^{3}+4f(x)=x3+4

Find the future value. -$4013 invested for 9 years at 4.1% compounded quarterly

Decide whether the pair of functions graphed are inverses. -

If the function is one-to-one, find its inverse. If not, write "not one-to-one." - f(x)=x−23f ( x ) = \sqrt [ 3 ] { x - 2 }f(x)=3x−2​

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Solve the problem. - $p ( t ) = 9270 e ^ { 0.004 t }$ , where t is the number of years. According to this formula, how many years will it take the population to double Its year 0 value? Round to the nearest tenth of a year.

For the function as defined that is one-to-one, graph f and $\mathbf { f } ^ { - 1 }$ on the same axes. - $f(x)=3 x$ $For the function as defined that is one-to-one, graph f and \mathbf { f } ^ { - 1 } on the same axes. - f(x)=3 x$

Find the value. Give an approximation to four decimal places. - $\ln \sqrt [ 5 ] { \mathrm { e } }$

Solve the equation. - $4 ^ { x - 3 } = 32 ^ { 4 x }$

Find the domain and range of the inverse of the given function. - $f ( x ) = x ^ { 3 } + 5$

Graph the function. - $f(x)=5|x|$

For the function as defined that is one-to-one, graph f and $\mathbf { f } ^ { - 1 }$ on the same axes. - $f(x)=x^{3}+4$ $For the function as defined that is one-to-one, graph f and \mathbf { f } ^ { - 1 } on the same axes. - f(x)=x^{3}+4$

If the function is one-to-one, find its inverse. If not, write "not one-to-one." - $f ( x ) = \sqrt [ 3 ] { x - 2 }$