Question 1

Determine whether the functions $f(x)$ and $g(x)$ are inverse functions.
-$f(x)=6 x+42, g(x)=\frac{1}{6}(x-42)$

Accepted Answer

A) True 
 B)False

Question 2

Graph. State the domain, range, and vertical asymptote of the function
-$f(x)=\log (x+4)+2$

Accepted Answer

A)  Domain: $ (-4, \infty) $, range: $ (-\infty, \infty) $ 
Vertical asymptote: $ \mathrm{x}=-4 $
  
B)  Domain: $ (-4, \infty) $, range: $ (-\infty, \infty) $ 
Vertical asymptote: $ \mathrm{x}=-4 $
  
C)  Domain: $ (0, \infty) $, range: $ (-\infty, \infty) $
 Vertical asymptote: $ x=0 $
  
D)  Domain: $ (0, \infty) $, range: $ (-\infty, \infty) $ 
Vertical asymptote: $ \mathrm{x}=0 $

Question 3

For the given function $f(x)$, find its inverse.
-$f(x)=\ln (x+3)+8$

Accepted Answer

A)  $\mathrm{f}^{-1}(\mathrm{x})=\mathrm{e}^{\mathrm{x}-8}-3$ 
B)  $\mathrm{f}^{-1}(\mathrm{x})=\mathrm{e}^{\mathrm{x}-3}-8$ 
C)  $f^{-1}(x)=e^{x-3}+8$ 
D)  $\mathrm{f}^{-1}(\mathrm{x})=\mathrm{e}^{\mathrm{x}-8}+3$ 
A)  $\mathrm{f}^{-1}(\mathrm{x})=\mathrm{e}^{\mathrm{x}-8}-3$ 
B)  $\mathrm{f}^{-1}(\mathrm{x})=\mathrm{e}^{\mathrm{x}-3}-8$ 
C)  $f^{-1}(x)=e^{x-3}+8$ 
D)  $\mathrm{f}^{-1}(\mathrm{x})=\mathrm{e}^{\mathrm{x}-8}+3$

Question 4

Find all intercepts for the given function. Round to the nearest tenth if necessary.
-$f(x)=e^{(x+2)}-4$

Accepted Answer

A)  $x$-int: $(-0.6,0)$; $y$-int: $(0,0.1)$ 
B)  $x$-int: $(-0.6,0)$; y-int: $(0,3.4)$ 
C)  $x$-int: $(0.7,0)$; $y$ - int: $(0,3.4)$ 
D)  $x$-int: $(3.4,0)$; $y$-int: $(0,-0.6)$ 
A)  $x$-int: $(-0.6,0)$; $y$-int: $(0,0.1)$ 
B)  $x$-int: $(-0.6,0)$; y-int: $(0,3.4)$ 
C)  $x$-int: $(0.7,0)$; $y$ - int: $(0,3.4)$ 
D)  $x$-int: $(3.4,0)$; $y$-int: $(0,-0.6)$

Question 5

Find the missing number. Round to the nearest hundredth if necessary.
-$20^ ?=89$

Accepted Answer

A)  0.67 
B)  1.50 
C)  2.49 
D)  0.65 
A)  0.67 
B)  1.50 
C)  2.49 
D)  0.65

Question 6

Rewrite as the sum of two or more logarithms using the product rule for logarithms. A ssume all variables represent positive real numbers.
-$\log _{2}(\mathrm{xy})$

Accepted Answer

A)  $\log _{1} \mathrm{x}-\log _{1} \mathrm{y}$ 
B)  $\log _{2} \mathrm{x}+\log _{2} \mathrm{y}$ 
C)  $\log _{2} \mathrm{x}-\log _{2} \mathrm{y}$ 
D)  $\log _{1} \mathrm{x}+\log _{1} \mathrm{y}$ 
A)  $\log _{1} \mathrm{x}-\log _{1} \mathrm{y}$ 
B)  $\log _{2} \mathrm{x}+\log _{2} \mathrm{y}$ 
C)  $\log _{2} \mathrm{x}-\log _{2} \mathrm{y}$ 
D)  $\log _{1} \mathrm{x}+\log _{1} \mathrm{y}$

Question 7

Rew rite as a single logarithm. A ssume all variables represent positive real numbers.
-$3 \log _{a} t-\log _{a} s$

Accepted Answer

A)  $\log _{a} \frac{t^{3}}{s}$ 
B)  $\log _{a}\left(t^{3}-s\right)$ 
C)  $\log _{a} t^{3} \div \log _{a} s$ 
D)  $\log _{a} \frac{3 t}{s}$ 
A)  $\log _{a} \frac{t^{3}}{s}$ 
B)  $\log _{a}\left(t^{3}-s\right)$ 
C)  $\log _{a} t^{3} \div \log _{a} s$ 
D)  $\log _{a} \frac{3 t}{s}$

Question 8

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

Accepted Answer

A) True 
 B)False

Question 9

Graph. State the domain, range, and horizontal asymptote of the function
-$f(x)=\left(\frac{1}{5}\right)^{x}+4$

Accepted Answer

A)  Domain: $ (-\infty, \infty) $, range: $ (-4, \infty) $
Horizontal asymptote: $ y=-4 $
  
B)  Domain: $ (-\infty, \infty) $, range: $ (0, \infty) $  
Horizontal asymptote: $ \mathrm{y}=0 $
  
C)  Domain: $ (-\infty, \infty) $, range: $ (0, \infty) $
Horizontal asymptote: $ \mathrm{y}=0 $ 
  
D)  Domain: $ (-\infty, \infty) $, range: $ (4, \infty) $ 
Horizontal asymptote: $ \mathrm{y}=4 $
  
A)  Domain: $ (-\infty, \infty) $, range: $ (-4, \infty) $
Horizontal asymptote: $ y=-4 $
  
B)  Domain: $ (-\infty, \infty) $, range: $ (0, \infty) $  
Horizontal asymptote: $ \mathrm{y}=0 $
  
C)  Domain: $ (-\infty, \infty) $, range: $ (0, \infty) $
Horizontal asymptote: $ \mathrm{y}=0 $ 
  
D)  Domain: $ (-\infty, \infty) $, range: $ (4, \infty) $ 
Horizontal asymptote: $ \mathrm{y}=4 $

Question 10

Graph a one-to-one function f(x) that meets the given criteria.
-$f(x)$ is a quadratic function, the domain of $f(x)$ is restricted to $[2, \infty), f^{-1}(-9)=2, f^{-1}(-8)=3$, and $\mathrm{f}^{-1}(-5)=4$.

Accepted Answer

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

Question 11

Solve.
-$\log 3 x=5$

Accepted Answer

A)  $\{15\}$ 
B)  $\{1.46\}$ 
C)  $\{125\}$ 
D)  $\{243\}$ 
A)  $\{15\}$ 
B)  $\{1.46\}$ 
C)  $\{125\}$ 
D)  $\{243\}$

Question 12

Rewrite in logarithmic form
-$3^{\mathrm{x}}=30$

Accepted Answer

A)  $\log _{3} x=30$ 
B)  $\log _{30} x=3$ 
C)  $\log _{3} 30=x$ 
D)  $\log _{30} 3=x$ 
A)  $\log _{3} x=30$ 
B)  $\log _{30} x=3$ 
C)  $\log _{3} 30=x$ 
D)  $\log _{30} 3=x$

Question 13

Find the specified domain
-For $f(x)=5 \sqrt{x+2}$ and $g(x)=4 x+18$, what is the domain of $f \circ g$ ?

Accepted Answer

A)  $[5, \infty)$ 
B)  $[-2, \infty)$ 
C)  $(-\infty,-5]$ 
D)  $[-5, \infty)$ 
A)  $[5, \infty)$ 
B)  $[-2, \infty)$ 
C)  $(-\infty,-5]$ 
D)  $[-5, \infty)$

Question 14

For the given graph of a one-to-one function f(x), graph its inverse functionf-1(x) using a dashed line
-

Accepted Answer

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

Question 15

Rewrite using the pow er and product rules. Assume all variables represent positive real numbers.
-$\ln x^{2} y^{4} z^{3}$

Accepted Answer

A)  $2 \ln x-4 \ln y-3 \ln z$ 
B)  $\ln \frac{2}{x}+\ln \frac{4}{y}+\ln \frac{3}{z}$ 
C)  $\ln 2 x+\ln 4 y+\ln 3 z$ 
D)  $2 \ln \mathrm{x}+4 \ln \mathrm{y}+3 \ln \mathrm{z}$ 
A)  $2 \ln x-4 \ln y-3 \ln z$ 
B)  $\ln \frac{2}{x}+\ln \frac{4}{y}+\ln \frac{3}{z}$ 
C)  $\ln 2 x+\ln 4 y+\ln 3 z$ 
D)  $2 \ln \mathrm{x}+4 \ln \mathrm{y}+3 \ln \mathrm{z}$

Question 16

Solve.
-$\log _{2}(2 x+8)=\log _{2}(2 x+3)$

Accepted Answer

A)  $\{5\}$ 
B)  $\{0\}$ 
C)  $\{2\}$ 
D)  $\varnothing$ 
A)  $\{5\}$ 
B)  $\{0\}$ 
C)  $\{2\}$ 
D)  $\varnothing$

Question 17

Expand. A ssume that all variables represent positive real numbers.
-$\log _{5}\left(\frac{\mathrm{x}^{3} \mathrm{y}^{9}}{3}\right)$

Accepted Answer

A)  $\left(3 \log _{5} \mathrm{x}\right)\left(9 \log _{5} \mathrm{y}\right)-\log _{5} 3$ 
B)  $3 \log _{5} x+9 \log _{5} y+\log _{5} 3$ 
C)  $3 \log _{5} x-9 \log _{5} y-\log _{5} 3$ 
D)  $3 \log _{5} \mathrm{x}+9 \log _{5} \mathrm{y}-\log _{5} 3$ 
A)  $\left(3 \log _{5} \mathrm{x}\right)\left(9 \log _{5} \mathrm{y}\right)-\log _{5} 3$ 
B)  $3 \log _{5} x+9 \log _{5} y+\log _{5} 3$ 
C)  $3 \log _{5} x-9 \log _{5} y-\log _{5} 3$ 
D)  $3 \log _{5} \mathrm{x}+9 \log _{5} \mathrm{y}-\log _{5} 3$

Question 18

For the given function $f(x)$, find $f^{-1}(x)$ and graph the function and its inverse.
-$f(x)=5^{x}$

Accepted Answer

A)  $ f(x)=5^{x}, f^{-1}(x)=\log _{5} x $
  
B)  $ f(x)=5^{x}, f^{-1}(x)=\log _{5} x $
  
C)  $ f(x)=5^{x}, f^{-1}(x)=\log _{5} x $
  
D)  $ f(x)=5^{x}, f^{-1}(x)=\log _{5} x $
  
A)  $ f(x)=5^{x}, f^{-1}(x)=\log _{5} x $
  
B)  $ f(x)=5^{x}, f^{-1}(x)=\log _{5} x $
  
C)  $ f(x)=5^{x}, f^{-1}(x)=\log _{5} x $
  
D)  $ f(x)=5^{x}, f^{-1}(x)=\log _{5} x $

Question 19

Graph f(x). State the domain, range, and horizontal asymptote of the function
-$f(x)=\left(\frac{1}{5}\right)^{x+1}$

Accepted Answer

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

Question 20

Graph f(x). State the domain, range, and horizontal asymptote of the function
-$f(x)=\left(\frac{1}{3}\right)^{x-2}+1$

Accepted Answer

A)  Domain: $ (-\infty, \infty) $, range: $ (-1, \infty) $
Horizontal asymptote: $ y=-1 $
  
B)  Domain: $ (-\infty, \infty) $, range: $ (-2, \infty) $  
Horizontal asymptote: $ \mathrm{y}=-2 $
  
C)  Domain: $ (-\infty, \infty) $, range: $ (2, \infty) $
 Horizontal asymptote: $ \mathrm{y}=2 $ 
  
D)  Domain: $ (-\infty, \infty) $, range: $ (1, \infty) $
Horizontal asymptote: $ \mathrm{y}=1 $
  
A)  Domain: $ (-\infty, \infty) $, range: $ (-1, \infty) $
Horizontal asymptote: $ y=-1 $
  
B)  Domain: $ (-\infty, \infty) $, range: $ (-2, \infty) $  
Horizontal asymptote: $ \mathrm{y}=-2 $
  
C)  Domain: $ (-\infty, \infty) $, range: $ (2, \infty) $
 Horizontal asymptote: $ \mathrm{y}=2 $ 
  
D)  Domain: $ (-\infty, \infty) $, range: $ (1, \infty) $
Horizontal asymptote: $ \mathrm{y}=1 $

Determine whether the functions $f(x)$ and $g(x)$ are inverse functions. - $f(x)=6 x+42, g(x)=\frac{1}{6}(x-42)$

Graph. State the domain, range, and vertical asymptote of the function - $f(x)=\log (x+4)+2$ $Graph. State the domain, range, and vertical asymptote of the function - f(x)=\log (x+4)+2$

For the given function $f(x)$ , find its inverse. - $f(x)=\ln (x+3)+8$

Find all intercepts for the given function. Round to the nearest tenth if necessary. - $f(x)=e^{(x+2)}-4$

Find the missing number. Round to the nearest hundredth if necessary. - $20^ ?=89$

Rewrite as the sum of two or more logarithms using the product rule for logarithms. A ssume all variables represent positive real numbers. - $\log _{2}(\mathrm{xy})$

Rew rite as a single logarithm. A ssume all variables represent positive real numbers. - $3 \log _{a} t-\log _{a} s$

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

Graph. State the domain, range, and horizontal asymptote of the function - $f(x)=\left(\frac{1}{5}\right)^{x}+4$ $Graph. State the domain, range, and horizontal asymptote of the function - f(x)=\left(\frac{1}{5}\right)^{x}+4$

Solve. - $\log 3 x=5$

Rewrite in logarithmic form - $3^{\mathrm{x}}=30$

Find the specified domain -For $f(x)=5 \sqrt{x+2}$ and $g(x)=4 x+18$ , what is the domain of $f \circ g$ ?

For the given graph of a one-to-one function f(x), graph its inverse functionf-1(x) using a dashed line -

Rewrite using the pow er and product rules. Assume all variables represent positive real numbers. - $\ln x^{2} y^{4} z^{3}$

Solve. - $\log _{2}(2 x+8)=\log _{2}(2 x+3)$

Expand. A ssume that all variables represent positive real numbers. - $\log _{5}\left(\frac{\mathrm{x}^{3} \mathrm{y}^{9}}{3}\right)$

For the given function $f(x)$ , find $f^{-1}(x)$ and graph the function and its inverse. - $f(x)=5^{x}$ $For the given function f(x) , find f^{-1}(x) and graph the function and its inverse. - f(x)=5^{x}$

Graph f(x). State the domain, range, and horizontal asymptote of the function - $f(x)=\left(\frac{1}{5}\right)^{x+1}$ $Graph f(x). State the domain, range, and horizontal asymptote of the function - f(x)=\left(\frac{1}{5}\right)^{x+1}$

Graph f(x). State the domain, range, and horizontal asymptote of the function - $f(x)=\left(\frac{1}{3}\right)^{x-2}+1$ $Graph f(x). State the domain, range, and horizontal asymptote of the function - f(x)=\left(\frac{1}{3}\right)^{x-2}+1$

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)=6x+42,g(x)=16(x−42)f(x)=6 x+42, g(x)=\frac{1}{6}(x-42)f(x)=6x+42,g(x)=61​(x−42)

Graph. State the domain, range, and vertical asymptote of the function - f(x)=log⁡(x+4)+2f(x)=\log (x+4)+2f(x)=log(x+4)+2

For the given function f(x)f(x)f(x) , find its inverse. - f(x)=ln⁡(x+3)+8f(x)=\ln (x+3)+8f(x)=ln(x+3)+8

Find all intercepts for the given function. Round to the nearest tenth if necessary. - f(x)=e(x+2)−4f(x)=e^{(x+2)}-4f(x)=e(x+2)−4

Find the missing number. Round to the nearest hundredth if necessary. - 20?=8920^ ?=8920?=89

Rewrite as the sum of two or more logarithms using the product rule for logarithms. A ssume all variables represent positive real numbers. - log⁡2(xy)\log _{2}(\mathrm{xy})log2​(xy)

Rew rite as a single logarithm. A ssume all variables represent positive real numbers. - 3log⁡at−log⁡as3 \log _{a} t-\log _{a} s3loga​t−loga​s