Question 1

Solve.
-$\log 101=\mathrm{x}$

Accepted Answer

A)  $\{1\}$ 
B)  $\{100\}$ 
C)  $\{10\}$ 
D)  $\{0\}$ 
A)  $\{1\}$ 
B)  $\{100\}$ 
C)  $\{10\}$ 
D)  $\{0\}$

Question 2

Solve.
-The number of books in a small library increases according to the function $B=6700 e^{0.04 t}$, where $t$ is measured in years. How many books will the library have after 5 years?

Accepted Answer

A)  4683 
B)  10,783 
C)  10,619 
D)  8183 
A)  4683 
B)  10,783 
C)  10,619 
D)  8183

Question 3

For the given exponential function, find a) the average rate of change for the interval $[3,5]$ and b) the interval $[3.5,4.5]$, as well as c) the rate of change at $x=4$. Round all calculations to the nearest hundredth.
-$f(x)=3^{x-4}$

Accepted Answer

A)  a) 1.38 b) 1.41 c) 1.45 
B)  a) 1.10 b) 1.15 c) 1.33 
C)  a) 1.45 b) 1.41 c) 1.38 
D)  a) 1.33
b) 1.15
c) 1.10 
A)  a) 1.38 b) 1.41 c) 1.45 
B)  a) 1.10 b) 1.15 c) 1.33 
C)  a) 1.45 b) 1.41 c) 1.38 
D)  a) 1.33
b) 1.15
c) 1.10

Question 4

For the given functions $f(x)$ and $g(x)$, find a value $x$ for which $(f\circ g)(x)=(g\circ f)(x)$.
-$f(x)=x-3, g(x)=5 x^{2}-8 x+5$

Accepted Answer

A)  $x=\frac{11}{5}$ 
B)  $x=\frac{4}{5}$ 
C)  $x=-\frac{12}{5}$ 
D)  $x=\frac{12}{5}$ 
A)  $x=\frac{11}{5}$ 
B)  $x=\frac{4}{5}$ 
C)  $x=-\frac{12}{5}$ 
D)  $x=\frac{12}{5}$

Question 5

Solve.
-There are currently 75 million cars in a certain country, increasing exponentially by $3.8 \%$ annually. How many years will it take for this country to have 90 million cars? Round to the nearest year.

Accepted Answer

A)  $3 \mathrm{yr}$ 
B)  $71 \mathrm{yr}$ 
C)  $4 \mathrm{yr}$ 
D)  $5 \mathrm{yr}$ 
A)  $3 \mathrm{yr}$ 
B)  $71 \mathrm{yr}$ 
C)  $4 \mathrm{yr}$ 
D)  $5 \mathrm{yr}$

Question 6

Determine the equation of the vertical asymptote for the graph of this function, and state the domain and range of this function.
-$f(x)=\ln (x-2)+5$

Accepted Answer

A)  Vertical asymptote: $\mathrm{x}=-5$;
Domain: $(-\infty,-5)$, Range: $(-\infty, \infty)$ 
B)  Vertical asymptote: $x=5$;
Domain: $(5, \infty)$, Range: $(-\infty, \infty)$ 
C)  Vertical asymptote: $\mathrm{x}=2$;
Domain: $(-\infty, 2)$, Range: $(-\infty, \infty)$ 
D)  Vertical asymptote: $\mathrm{x}=2$;
Domain: $(2, \infty)$, Range: $(-\infty, \infty)$ 
A)  Vertical asymptote: $\mathrm{x}=-5$;
Domain: $(-\infty,-5)$, Range: $(-\infty, \infty)$ 
B)  Vertical asymptote: $x=5$;
Domain: $(5, \infty)$, Range: $(-\infty, \infty)$ 
C)  Vertical asymptote: $\mathrm{x}=2$;
Domain: $(-\infty, 2)$, Range: $(-\infty, \infty)$ 
D)  Vertical asymptote: $\mathrm{x}=2$;
Domain: $(2, \infty)$, Range: $(-\infty, \infty)$

Question 7

Graph f(x). State the domain, range, and horizontal asymptote of the function
-$f(x)=\left(\frac{1}{4}\right)^{x}$

Accepted Answer

A)  Domain: $ (-\infty, \infty) $, range: $ (-\infty, 0) $
Horizontal asymptote: $ \mathrm{y}=0 $
  
B)  Domain: $ (-\infty, \infty) $, range: $ (0, \infty) $
Horizontal asymptote: $ \mathrm{y}=0 $
  
C)  Domain: $ (-\infty, \infty) $, range: $ (0, \infty) $
Horizontal asymptote: $ y=0 $
  
D)  Domain: $ (-\infty, \infty) $, range: $ (-\infty, 0) $ 
Horizontal asymptote: $ y=0 $ 
  
A)  Domain: $ (-\infty, \infty) $, range: $ (-\infty, 0) $
Horizontal asymptote: $ \mathrm{y}=0 $
  
B)  Domain: $ (-\infty, \infty) $, range: $ (0, \infty) $
Horizontal asymptote: $ \mathrm{y}=0 $
  
C)  Domain: $ (-\infty, \infty) $, range: $ (0, \infty) $
Horizontal asymptote: $ y=0 $
  
D)  Domain: $ (-\infty, \infty) $, range: $ (-\infty, 0) $ 
Horizontal asymptote: $ y=0 $

Question 8

The number of visitors to a tourist attraction (for the first few years after its opening) can be approximated by $\mathrm{V}(\mathrm{x})=50+10 \log _{2} \mathrm{x}$, where $\mathrm{x}$ represents the number of months after the opening of the attraction. Find the number of visitors 8 months after the opening of the attraction.

Accepted Answer

A)  130 visitors 
B)  53 visitors 
C)  58 visitors 
D)  80 visitors 
A)  130 visitors 
B)  53 visitors 
C)  58 visitors 
D)  80 visitors

Question 9

Evaluate the given function.
-$f(x)=\log _{4} x, f\left(\frac{1}{64}\right)$

Accepted Answer

A)  3 
B)  -3 
C)  -4 
D)  4 
A)  3 
B)  -3 
C)  -4 
D)  4

Question 10

An earthquake was recorded with a shock wave which was 7,943,282 times more powerful than the smallest measurable shock wave recordable by a seismograph. What is the magnitude of this earthquake on the Richter scale (rounded to the nearest tenth)? The magnitude on the Richter scale of an earthquake of intensity I is logI.

Accepted Answer

A)  6.9 
B)  0.7 
C)  15.9 
D)  5.9 
A)  6.9 
B)  0.7 
C)  15.9 
D)  5.9

Question 11

Given $f(x)$ and $g(x)$, find the indicated composition and state its domain.
-$f(x)=\frac{x-5}{3} ; g(x)=3 x+5$
Find $(\mathrm{g} \circ \mathrm{f})(\mathrm{x})$.

Accepted Answer

A)  $x$, all real numbers 
B)  $x-\frac{5}{3}$, all real numbers 
C)  $x+10$, all real numbers 
D)  $3 x+10$, all real numbers 
A)  $x$, all real numbers 
B)  $x-\frac{5}{3}$, all real numbers 
C)  $x+10$, all real numbers 
D)  $3 x+10$, all real numbers

Question 12

Determine whether function is one-to-one.
-$\{(-5,4),(-18,11),(-19,-8)\}$

Accepted Answer

A) True 
 B)False

Question 13

For the given function $g(x)$, find a function $f(x)$ such that $(f \circ g)(x)=x$.
-$g(x)=-18 x$

Accepted Answer

A)  $f(x)=18 x$ 
B)  $f(x)=-\frac{x}{18}$ 
C)  $f(x)=-\frac{x}{18}$. 
D)  $f(x)=-\frac{18}{x}$ 
A)  $f(x)=18 x$ 
B)  $f(x)=-\frac{x}{18}$ 
C)  $f(x)=-\frac{x}{18}$. 
D)  $f(x)=-\frac{18}{x}$

Question 14

For the given functions $f(x)$ and $g(x)$, find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated.
-$f(x)=2 x-8, g(x)=7 x-3$
Find $(f \cdot g)(x)$.

Accepted Answer

A)  $14 x^{2}-59 x+24$ 
B)  $14 x^{2}+24$ 
C)  $14 x^{2}-62 x+24$ 
D)  $9 x^{2}-62 x-11$ 
A)  $14 x^{2}-59 x+24$ 
B)  $14 x^{2}+24$ 
C)  $14 x^{2}-62 x+24$ 
D)  $9 x^{2}-62 x-11$

Question 15

Graph the given function f(x). Label the vertical asymptote. State the domain and range of the function.
-Let $\mathrm{f}(\mathrm{x})=\log (\mathrm{x}-14)-6$. Solve $\mathrm{f}(\mathrm{x})=-3$.

Accepted Answer

A)  $\{14.001\}$ 
B)  $\{986\}$ 
C)  $\{1,000,014\}$ 
D)  $\{1014\}$ 
A)  $\{14.001\}$ 
B)  $\{986\}$ 
C)  $\{1,000,014\}$ 
D)  $\{1014\}$

Question 16

Solve the problem.
-Use the formula $L=10 \cdot \log \frac{I}{I_{0}}$, where the loudness of a sound in decibels is determined by $I$, the number of watts per square meter produced by the sound wave, and $\mathrm{I}_{0}=10^{-12}$ watts per square meter. A certain noise produces $5.34 \times 10^{-4}$ watts per square meter of power. What is the decibel level of this noise?

Accepted Answer

A)  $77 \mathrm{db}$ 
B)  $201 \mathrm{db}$ 
C)  $9 \mathrm{db}$ 
D)  $87 \mathrm{db}$ 
A)  $77 \mathrm{db}$ 
B)  $201 \mathrm{db}$ 
C)  $9 \mathrm{db}$ 
D)  $87 \mathrm{db}$

Question 17

Solve.
-$\log _{4} x^{2}=\log _{4}(2 x+15)$

Accepted Answer

A)  $\varnothing$ 
B)  $\{-3\}$ 
C)  $\{5,-3\}$ 
D)  $\{5\}$ 
A)  $\varnothing$ 
B)  $\{-3\}$ 
C)  $\{5,-3\}$ 
D)  $\{5\}$

Question 18

Determine whether the graph is the graph of a function.
-

Accepted Answer

A) True 
 B)False

Question 19

Solve.
-$\ln \left(x^{2}+9 x-49\right)=\ln (5 x-4)$

Accepted Answer

A)  $\{5\}$ 
B)  $\varnothing$ 
C)  $\{-9,5\}$ 
D)  $\{5,9\}$ 
A)  $\{5\}$ 
B)  $\varnothing$ 
C)  $\{-9,5\}$ 
D)  $\{5,9\}$

Question 20

For the given functions $f(x)$ and $g(x)$, find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated.
-$f(x)=2 x+1, g(x)=x-7$
Find $\left(\frac{f}{g}\right)(x)$.

Accepted Answer

A)  $\frac{2 x+1}{x-7}$ 
B)  $\frac{x-7}{2 x+1}$ 
C)  $2-\frac{x}{7}$ 
D)  $2 x-\frac{1}{7}$ 
A)  $\frac{2 x+1}{x-7}$ 
B)  $\frac{x-7}{2 x+1}$ 
C)  $2-\frac{x}{7}$ 
D)  $2 x-\frac{1}{7}$

Solve. - $\log 101=\mathrm{x}$

Solve. -The number of books in a small library increases according to the function $B=6700 e^{0.04 t}$ , where $t$ is measured in years. How many books will the library have after 5 years?

For the given exponential function, find a) the average rate of change for the interval $[3,5]$ and b) the interval $[3.5,4.5]$ , as well as c) the rate of change at $x=4$ . Round all calculations to the nearest hundredth. - $f(x)=3^{x-4}$

For the given functions $f(x)$ and $g(x)$ , find a value $x$ for which $(f\circ g)(x)=(g\circ f)(x)$ . - $f(x)=x-3, g(x)=5 x^{2}-8 x+5$

Solve. -There are currently 75 million cars in a certain country, increasing exponentially by $3.8 \%$ annually. How many years will it take for this country to have 90 million cars? Round to the nearest year.

Determine the equation of the vertical asymptote for the graph of this function, and state the domain and range of this function. - $f(x)=\ln (x-2)+5$

Graph f(x). State the domain, range, and horizontal asymptote of the function - $f(x)=\left(\frac{1}{4}\right)^{x}$ $Graph f(x). State the domain, range, and horizontal asymptote of the function - f(x)=\left(\frac{1}{4}\right)^{x}$

Evaluate the given function. - $f(x)=\log _{4} x, f\left(\frac{1}{64}\right)$

Given $f(x)$ and $g(x)$ , find the indicated composition and state its domain. - $f(x)=\frac{x-5}{3} ; g(x)=3 x+5$ Find $(\mathrm{g} \circ \mathrm{f})(\mathrm{x})$ .

Determine whether function is one-to-one. - $\{(-5,4),(-18,11),(-19,-8)\}$

For the given function $g(x)$ , find a function $f(x)$ such that $(f \circ g)(x)=x$ . - $g(x)=-18 x$

For the given functions $f(x)$ and $g(x)$ , find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated. - $f(x)=2 x-8, g(x)=7 x-3$ Find $(f \cdot g)(x)$ .

Graph the given function f(x). Label the vertical asymptote. State the domain and range of the function. -Let $\mathrm{f}(\mathrm{x})=\log (\mathrm{x}-14)-6$ . Solve $\mathrm{f}(\mathrm{x})=-3$ .

Solve. - $\log _{4} x^{2}=\log _{4}(2 x+15)$

Determine whether the graph is the graph of a function. -

Solve. - $\ln \left(x^{2}+9 x-49\right)=\ln (5 x-4)$

For the given functions $f(x)$ and $g(x)$ , find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated. - $f(x)=2 x+1, g(x)=x-7$ Find $\left(\frac{f}{g}\right)(x)$ .

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Systems of Equations

Exponents, Polynomials, and Factoring Polynomials

Rational Expressions and Equations

Radical Expressions and Equations

Quadratic Equations

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 9: Logarithmic and Exponential Functions

Solve. - log⁡101=x\log 101=\mathrm{x}log101=x

Solve. -The number of books in a small library increases according to the function B=6700e0.04tB=6700 e^{0.04 t}B=6700e0.04t , where ttt is measured in years. How many books will the library have after 5 years?

For the given exponential function, find a) the average rate of change for the interval [3,5][3,5][3,5] and b) the interval [3.5,4.5][3.5,4.5][3.5,4.5] , as well as c) the rate of change at x=4x=4x=4 . Round all calculations to the nearest hundredth. - f(x)=3x−4f(x)=3^{x-4}f(x)=3x−4

For the given functions f(x)f(x)f(x) and g(x)g(x)g(x) , find a value xxx for which (f∘g)(x)=(g∘f)(x)(f\circ g)(x)=(g\circ f)(x)(f∘g)(x)=(g∘f)(x) . - f(x)=x−3,g(x)=5x2−8x+5f(x)=x-3, g(x)=5 x^{2}-8 x+5f(x)=x−3,g(x)=5x2−8x+5

Solve. -There are currently 75 million cars in a certain country, increasing exponentially by 3.8%3.8 \%3.8% annually. How many years will it take for this country to have 90 million cars? Round to the nearest year.

Determine the equation of the vertical asymptote for the graph of this function, and state the domain and range of this function. - f(x)=ln⁡(x−2)+5f(x)=\ln (x-2)+5f(x)=ln(x−2)+5

Graph f(x). State the domain, range, and horizontal asymptote of the function - f(x)=(14)xf(x)=\left(\frac{1}{4}\right)^{x}f(x)=(41​)x

Evaluate the given function. - f(x)=log⁡4x,f(164)f(x)=\log _{4} x, f\left(\frac{1}{64}\right)f(x)=log4​x,f(641​)

Given f(x)f(x)f(x) and g(x)g(x)g(x) , find the indicated composition and state its domain. - f(x)=x−53;g(x)=3x+5f(x)=\frac{x-5}{3} ; g(x)=3 x+5f(x)=3x−5​;g(x)=3x+5 Find (g∘f)(x)(\mathrm{g} \circ \mathrm{f})(\mathrm{x})(g∘f)(x) .

Determine whether function is one-to-one. - {(−5,4),(−18,11),(−19,−8)}\{(-5,4),(-18,11),(-19,-8)\}{(−5,4),(−18,11),(−19,−8)}

For the given function g(x)g(x)g(x) , find a function f(x)f(x)f(x) such that (f∘g)(x)=x(f \circ g)(x)=x(f∘g)(x)=x . - g(x)=−18xg(x)=-18 xg(x)=−18x

For the given functions f(x)f(x)f(x) and g(x)g(x)g(x) , find (f⋅g)(x)(f \cdot g)(x)(f⋅g)(x) or (fg)(x)\left(\frac{f}{g}\right)(x)(gf​)(x) as indicated. - f(x)=2x−8,g(x)=7x−3f(x)=2 x-8, g(x)=7 x-3f(x)=2x−8,g(x)=7x−3 Find (f⋅g)(x)(f \cdot g)(x)(f⋅g)(x) .

Graph the given function f(x). Label the vertical asymptote. State the domain and range of the function. -Let f(x)=log⁡(x−14)−6\mathrm{f}(\mathrm{x})=\log (\mathrm{x}-14)-6f(x)=log(x−14)−6 . Solve f(x)=−3\mathrm{f}(\mathrm{x})=-3f(x)=−3 .

Solve. - log⁡4x2=log⁡4(2x+15)\log _{4} x^{2}=\log _{4}(2 x+15)log4​x2=log4​(2x+15)