Question 1

Determine whether the functions $f(x)$ and $g(x)$ are inverse functions.
-$f(x)=-\frac{2}{x}$

Accepted Answer

A)  $f^{-1}(x)=\frac{2}{x}$ 
B)  $f^{-1}(x)=-2 x$ 
C)  $f^{-1}(x)=-\frac{x}{2}$ 
D)  $\mathrm{f}^{-1}(\mathrm{x})=-\frac{2}{\mathrm{x}}$ 
A)  $f^{-1}(x)=\frac{2}{x}$ 
B)  $f^{-1}(x)=-2 x$ 
C)  $f^{-1}(x)=-\frac{x}{2}$ 
D)  $\mathrm{f}^{-1}(\mathrm{x})=-\frac{2}{\mathrm{x}}$

Question 2

Solve the problem.
-The hydrogen ion concentration of a substance $\left[\mathrm{H}^{\dagger}\right]$ is about $2.9 \times 10^{-12}$ moles per liter. Find the $\mathrm{pH}$. Round to the nearest tenth. Use the formula $\mathrm{pH}=-\log \left[\mathrm{H}^{+}\right]$.

Accepted Answer

A)  11.8 
B)  11.5 
C)  12.5 
D)  -12.5 
A)  11.8 
B)  11.5 
C)  12.5 
D)  -12.5

Question 3

Determine the equation of the vertical asymptote for the graph of this function, and state the domain and range of this function.
-$f(x)=\log (2 x+1)+12$

Accepted Answer

A)  Vertical asymptote: $x=-\frac{1}{2}$;
Domain: $\left(-\frac{1}{2}, \infty\right)$, Range: $(-\infty, \infty)$ 
B)  Vertical asymptote: $\mathrm{x}=-2$;
Domain: $(-2, \infty)$, Range: $(-\infty, \infty)$ 
C)  Vertical asymptote: $x=\frac{1}{2}$;
Domain: $\left(\frac{1}{2}, \infty\right)$, Range: $(-\infty, \infty)$ 
D)  Vertical asymptote: $\mathrm{x}=-12$;
Domain: $(-12, \infty)$, Range: $(-\infty, \infty)$ 
A)  Vertical asymptote: $x=-\frac{1}{2}$;
Domain: $\left(-\frac{1}{2}, \infty\right)$, Range: $(-\infty, \infty)$ 
B)  Vertical asymptote: $\mathrm{x}=-2$;
Domain: $(-2, \infty)$, Range: $(-\infty, \infty)$ 
C)  Vertical asymptote: $x=\frac{1}{2}$;
Domain: $\left(\frac{1}{2}, \infty\right)$, Range: $(-\infty, \infty)$ 
D)  Vertical asymptote: $\mathrm{x}=-12$;
Domain: $(-12, \infty)$, Range: $(-\infty, \infty)$

Question 4

Simplify.
-$7^{\log 7} 3$

Accepted Answer

A)  -7 
B)  343 
C)  3 
D)  -3 
A)  -7 
B)  343 
C)  3 
D)  -3

Question 5

Find the specified domain
-For $f(x)=2 x-5$ and $g(x)=\sqrt{x+8}$, what is the domain of $f \circ g$ ?

Accepted Answer

A)  $(-8,8)$ 
B)  $[-8, \infty)$ 
C)  $[0, \infty)$ 
D)  $[8, \infty)$ 
A)  $(-8,8)$ 
B)  $[-8, \infty)$ 
C)  $[0, \infty)$ 
D)  $[8, \infty)$

Question 6

Rewrite in logarithmic form
-$10^{-5}=0.00001$

Accepted Answer

A)  $\log 0.00001=-5$ 
B)  $\log _{5} 0.10=-5$ 
C)  $\log -5=0.00001$ 
D)  $\log _{5}-5=0.10$ 
A)  $\log 0.00001=-5$ 
B)  $\log _{5} 0.10=-5$ 
C)  $\log -5=0.00001$ 
D)  $\log _{5}-5=0.10$

Question 7

Determine the equation of the vertical asymptote for the graph of this function, and state the domain and range of this function.
-$f(x)=\log _{3}(x+2)-2$

Accepted Answer

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

Question 8

Determine whether the functions $f(x)$ and $g(x)$ are inverse functions.
-$f(x)=6 x+7 g(x)=\frac{1}{6} x-7$

Accepted Answer

A) True 
 B)False

Question 9

Given $f(x)$ and $g(x)$, find the indicated composition and state its domain.
-$f(x)=\frac{2 x+3}{5 x-8}, g(x)=x-8$
Find $(\mathrm{f} \circ g)(\mathrm{x})$ and state its domain.

Accepted Answer

A)  $\frac{2 x+13}{5 x+48}$, all real numbers except $-\frac{48}{5}$. 
B)  $\frac{2 x-13}{5 x-48}$, all real numbers exœpt $\frac{48}{5}$. 
C)  $\frac{2 x+5}{5 x+16}$, all real numbers except $-\frac{16}{5}$. 
D)  $\frac{2 x-5}{5 x-16}$, all real numbers except $\frac{16}{5}$. 
A)  $\frac{2 x+13}{5 x+48}$, all real numbers except $-\frac{48}{5}$. 
B)  $\frac{2 x-13}{5 x-48}$, all real numbers exœpt $\frac{48}{5}$. 
C)  $\frac{2 x+5}{5 x+16}$, all real numbers except $-\frac{16}{5}$. 
D)  $\frac{2 x-5}{5 x-16}$, all real numbers except $\frac{16}{5}$.

Question 10

Suppose for some base $b>0(b \neq 1)$ that $\log _{b} 2=A, \log _{b} 3=B, \log _{b} 5=C$, and $\log _{b} 7=D$. Express the given logarithms in terms of A, B, C, or D.
-$\log _{b} 21$

Accepted Answer

A)  $B+D$ 
B)  $\mathrm{B}+\mathrm{C}$ 
C)  $A+B$ 
D)  $A+D$ 
A)  $B+D$ 
B)  $\mathrm{B}+\mathrm{C}$ 
C)  $A+B$ 
D)  $A+D$

Question 11

Another way to approximate the value of $e$ is through the sum $1+\frac{1}{1 !}+\frac{1}{2 !}+\frac{1}{3 !}+\ldots$. The notation $n !$ represents $n$ factorial, which is the product of all the integers from 1 through $n$. The more terms added to the sum, the closer the sum gets to e. In calculus, we say that the limit of this sum is e. Find the sum of the first $k$ terms, rounded to the nearest hundred-thousandth, and determine how close the result is to e rounded to the nearest hundred-thousandth (2.71828).
-$\mathrm{k}=5$ terms

Accepted Answer

A)  $2.71828,0$ 
B)  $2.71667,0.00161$ 
C)  $2.70833,0.00995$ 
D)  $2.5,0.21828$ 
A)  $2.71828,0$ 
B)  $2.71667,0.00161$ 
C)  $2.70833,0.00995$ 
D)  $2.5,0.21828$

Question 12

Determine whether function is one-to-one.
-$\begin{array}{l|l|l|l}
\mathrm{x} & -17 & 17 & 6 \
\hline \mathrm{f}(\mathrm{x}) & 8 & -3 & -14 \
\hline
\end{array}$

Accepted Answer

A) True 
 B)False

Question 13

Solve the equation.
-$\ln (5 x-6)=\ln 36-\ln (x-6)$

Accepted Answer

A)  $\varnothing$ 
B)  $\left\{6, \frac{6}{5}\right\}$ 
C)  $\left\{\frac{36}{5}\right\}$ 
D)  $\left\{0, \frac{36}{5}\right\}$ 
A)  $\varnothing$ 
B)  $\left\{6, \frac{6}{5}\right\}$ 
C)  $\left\{\frac{36}{5}\right\}$ 
D)  $\left\{0, \frac{36}{5}\right\}$

Question 14

Rewrite as a single logarithm using the quotient rule for logarithms. Assume all variables represent positive real numbers.
-$\log _{\mathrm{a}} 1,000,000$ - $\log _{\mathrm{a}} 1000$

Accepted Answer

A)  $1000 \log _{a} 1,000,000$ 
B)  $\log _{a} \frac{1}{1000}$ 
C)  $\log _{a} 999,000$ 
D)  $\log _{a} 1000$ 
A)  $1000 \log _{a} 1,000,000$ 
B)  $\log _{a} \frac{1}{1000}$ 
C)  $\log _{a} 999,000$ 
D)  $\log _{a} 1000$

Question 15

Express $h(x)$ as a composition of two functions $f(x)$ and $g(x)$ : (f $\circ g)(x)$. A nsw ers may vary. Choose the possible answer.
-$h(x)=5 \sqrt{6 x-17}+10$

Accepted Answer

A)  $f(x)=5 \sqrt{x+10}, g(x)=6 x-17$ 
B)  $f(x)=5 \sqrt{x}+10, g(x)=6 x-17$ 
C)  $f(x)=5 \sqrt{x}, g(x)=6 x-7$ 
D)  $f(x)=5 \sqrt{x+10}, g(x)=6 x-7$ 
A)  $f(x)=5 \sqrt{x+10}, g(x)=6 x-17$ 
B)  $f(x)=5 \sqrt{x}+10, g(x)=6 x-17$ 
C)  $f(x)=5 \sqrt{x}, g(x)=6 x-7$ 
D)  $f(x)=5 \sqrt{x+10}, g(x)=6 x-7$

Question 16

Evaluate the given function
-$f(x)=5^{x}+3, f(3)$

Accepted Answer

A)  125 
B)  15,625 
C)  128 
D)  18 
A)  125 
B)  15,625 
C)  128 
D)  18

Question 17

Suppose for some base $b>0(b \neq 1)$ that $\log _{b} 2=A, \log _{b} 3=B, \log _{b} 5=C$, and $\log _{b} 7=D$. Express the given logarithms in terms of A, B, C, or D.
-$\log _{b}\left(\frac{1}{343}\right)$

Accepted Answer

A)  $3 \mathrm{D}$ 
B)  - 3D 
C)  $3 \mathrm{~A}$ 
D)  - 3A 
A)  $3 \mathrm{D}$ 
B)  - 3D 
C)  $3 \mathrm{~A}$ 
D)  - 3A

Question 18

For the given function $f(x)$, find $f^{-1}(x)$. State the domain of $f^{-1}(x)$.
-$f(x)=(x-3)^{2}(x \geq 3)$

Accepted Answer

A)  $f-1(x)=\sqrt{x+3}, x \geq-3$ 
B)  $f^{-1}(x)=\sqrt{x^{2}+3}, x \geq-3$ 
C)  $f^{1}(x)=\sqrt{x}+3, x \geq 0$ 
D)  $f^{-1}(x)=x^{2}+3, x \geq-3$ 
A)  $f-1(x)=\sqrt{x+3}, x \geq-3$ 
B)  $f^{-1}(x)=\sqrt{x^{2}+3}, x \geq-3$ 
C)  $f^{1}(x)=\sqrt{x}+3, x \geq 0$ 
D)  $f^{-1}(x)=x^{2}+3, x \geq-3$

Question 19

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of thisfunction.
-$f(x)=3^{x-2}$

Accepted Answer

A)  Horizontal asymptote: $\mathrm{y}=-2$;
Domain: $(-\infty, \infty)$, Range: $(-2, \infty)$ 
B)  Horizontal asymptote: $\mathrm{y}=0$;
Domain: $(-\infty, \infty)$, Range: $(0, \infty)$ 
C)  Horizontal asymptote: $\mathrm{y}=2$;
Domain: $(-\infty, \infty)$, Range: $(2, \infty)$ 
D)  Horizontal asymptote: $\mathrm{y}=3$;
Domain: $(-\infty, \infty)$, Range: $(3, \infty)$ 
A)  Horizontal asymptote: $\mathrm{y}=-2$;
Domain: $(-\infty, \infty)$, Range: $(-2, \infty)$ 
B)  Horizontal asymptote: $\mathrm{y}=0$;
Domain: $(-\infty, \infty)$, Range: $(0, \infty)$ 
C)  Horizontal asymptote: $\mathrm{y}=2$;
Domain: $(-\infty, \infty)$, Range: $(2, \infty)$ 
D)  Horizontal asymptote: $\mathrm{y}=3$;
Domain: $(-\infty, \infty)$, Range: $(3, \infty)$

Question 20

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of thisfunction.
-$f(x)=e^{3 x}-1$

Accepted Answer

A)  Horizontal asymptote: $\mathrm{y}=1$;
Domain: $(-\infty, \infty)$, Range: $(1, \infty)$ 
B)  Horizontal asymptote: $\mathrm{y}=0$;
Domain: $(-\infty, \infty)$, Range: $(0, \infty)$ 
C)  Horizontal asymptote: $\mathrm{y}=3$;
Domain: $(-\infty, \infty)$, Range: $(3, \infty)$ 
D)  Horizontal asymptote: $\mathrm{y}=-1$;
Domain: $(-\infty, \infty)$, Range: $(-1, \infty)$ 
A)  Horizontal asymptote: $\mathrm{y}=1$;
Domain: $(-\infty, \infty)$, Range: $(1, \infty)$ 
B)  Horizontal asymptote: $\mathrm{y}=0$;
Domain: $(-\infty, \infty)$, Range: $(0, \infty)$ 
C)  Horizontal asymptote: $\mathrm{y}=3$;
Domain: $(-\infty, \infty)$, Range: $(3, \infty)$ 
D)  Horizontal asymptote: $\mathrm{y}=-1$;
Domain: $(-\infty, \infty)$, Range: $(-1, \infty)$

Determine whether the functions $f(x)$ and $g(x)$ are inverse functions. - $f(x)=-\frac{2}{x}$

Solve the problem. -The hydrogen ion concentration of a substance $\left[\mathrm{H}^{\dagger}\right]$ is about $2.9 \times 10^{-12}$ moles per liter. Find the $\mathrm{pH}$ . Round to the nearest tenth. Use the formula $\mathrm{pH}=-\log \left[\mathrm{H}^{+}\right]$ .

Determine the equation of the vertical asymptote for the graph of this function, and state the domain and range of this function. - $f(x)=\log (2 x+1)+12$

Simplify. - $7^{\log 7} 3$

Find the specified domain -For $f(x)=2 x-5$ and $g(x)=\sqrt{x+8}$ , what is the domain of $f \circ g$ ?

Rewrite in logarithmic form - $10^{-5}=0.00001$

Determine the equation of the vertical asymptote for the graph of this function, and state the domain and range of this function. - $f(x)=\log _{3}(x+2)-2$

Determine whether the functions $f(x)$ and $g(x)$ are inverse functions. - $f(x)=6 x+7 g(x)=\frac{1}{6} x-7$

Given $f(x)$ and $g(x)$ , find the indicated composition and state its domain. - $f(x)=\frac{2 x+3}{5 x-8}, g(x)=x-8$ Find $(\mathrm{f} \circ g)(\mathrm{x})$ and state its domain.

Suppose for some base $b>0(b \neq 1)$ that $\log _{b} 2=A, \log _{b} 3=B, \log _{b} 5=C$ , and $\log _{b} 7=D$ . Express the given logarithms in terms of A, B, C, or D. - $\log _{b} 21$

Determine whether function is one-to-one. - -17 17 6 () 8 -3 -14

Solve the equation. - $\ln (5 x-6)=\ln 36-\ln (x-6)$

Rewrite as a single logarithm using the quotient rule for logarithms. Assume all variables represent positive real numbers. - $\log _{\mathrm{a}} 1,000,000$ - $\log _{\mathrm{a}} 1000$

Express $h(x)$ as a composition of two functions $f(x)$ and $g(x)$ : (f $\circ g)(x)$ . A nsw ers may vary. Choose the possible answer. - $h(x)=5 \sqrt{6 x-17}+10$

Evaluate the given function - $f(x)=5^{x}+3, f(3)$

Suppose for some base $b>0(b \neq 1)$ that $\log _{b} 2=A, \log _{b} 3=B, \log _{b} 5=C$ , and $\log _{b} 7=D$ . Express the given logarithms in terms of A, B, C, or D. - $\log _{b}\left(\frac{1}{343}\right)$

For the given function $f(x)$ , find $f^{-1}(x)$ . State the domain of $f^{-1}(x)$ . - $f(x)=(x-3)^{2}(x \geq 3)$

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of thisfunction. - $f(x)=3^{x-2}$

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of thisfunction. - $f(x)=e^{3 x}-1$

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

Determine whether the functions f(x)f(x)f(x) and g(x)g(x)g(x) are inverse functions. - f(x)=−2xf(x)=-\frac{2}{x}f(x)=−x2​

Determine the equation of the vertical asymptote for the graph of this function, and state the domain and range of this function. - f(x)=log⁡(2x+1)+12f(x)=\log (2 x+1)+12f(x)=log(2x+1)+12

Simplify. - 7log⁡737^{\log 7} 37log73

Find the specified domain -For f(x)=2x−5f(x)=2 x-5f(x)=2x−5 and g(x)=x+8g(x)=\sqrt{x+8}g(x)=x+8​ , what is the domain of f∘gf \circ gf∘g ?

Rewrite in logarithmic form - 10−5=0.0000110^{-5}=0.0000110−5=0.00001

Determine the equation of the vertical asymptote for the graph of this function, and state the domain and range of this function. - f(x)=log⁡3(x+2)−2f(x)=\log _{3}(x+2)-2f(x)=log3​(x+2)−2

Determine whether the functions f(x)f(x)f(x) and g(x)g(x)g(x) are inverse functions. - f(x)=6x+7g(x)=16x−7f(x)=6 x+7 g(x)=\frac{1}{6} x-7f(x)=6x+7g(x)=61​x−7

Given f(x)f(x)f(x) and g(x)g(x)g(x) , find the indicated composition and state its domain. - f(x)=2x+35x−8,g(x)=x−8f(x)=\frac{2 x+3}{5 x-8}, g(x)=x-8f(x)=5x−82x+3​,g(x)=x−8 Find (f∘g)(x)(\mathrm{f} \circ g)(\mathrm{x})(f∘g)(x) and state its domain.