Question 1

Rewrite in exponential form.
-$\log 100.01=-2$

Accepted Answer

A)  $10^{-2}=.1$ 
B)  $10^{2}=.1$ 
C)  $10^{2}=0.01$ 
D)  $10^{-2}=0.01$ 
A)  $10^{-2}=.1$ 
B)  $10^{2}=.1$ 
C)  $10^{2}=0.01$ 
D)  $10^{-2}=0.01$

Question 2

Evaluate the given function. Round to the nearest thousandth.
-$f(x)=e^{x}, f(1.3)$

Accepted Answer

A)  3.669 
B)  4.055 
C)  0.470 
D)  0.262 
A)  3.669 
B)  4.055 
C)  0.470 
D)  0.262

Question 3

Graph the given function f(x). Label the vertical asymptote. State the domain and range of the function.
-$f(x)=\log _{1 / 4} x$

Accepted Answer

A)  Vertical Asymptote: $ y=0 $;
Domain: $ (-\infty, \infty) $; Range: $ (0, \infty) $
  
B)  Vertical Asymptote: $ x=0 $;
Domain: $ (0, \infty) $; Range: $ (-\infty, \infty) $
  
C)  Vertical Asymptote: $ x=0 $; 
Domain: $ (0, \infty) $; Range: $ (\infty, -\infty) $
  
D)  Vertical Asymptote: $ \mathrm{y}=0 $; 
Domain: $ (-\infty, \infty) $; Range: $ (-\infty, 0) $
  
A)  Vertical Asymptote: $ y=0 $;
Domain: $ (-\infty, \infty) $; Range: $ (0, \infty) $
  
B)  Vertical Asymptote: $ x=0 $;
Domain: $ (0, \infty) $; Range: $ (-\infty, \infty) $
  
C)  Vertical Asymptote: $ x=0 $; 
Domain: $ (0, \infty) $; Range: $ (\infty, -\infty) $
  
D)  Vertical Asymptote: $ \mathrm{y}=0 $; 
Domain: $ (-\infty, \infty) $; Range: $ (-\infty, 0) $

Question 4

Rewrite using the pow er and product rules. Assume all variables represent positive real numbers.
-$\log _{\mathrm{b}} \mathrm{yz}^{5}$

Accepted Answer

A)  $5 \log _{b} y+5 \log _{b} z$ 
B)  $\log _{b} y+\log _{b} 5 z$ 
C)  $\log _{b} y+5 \log _{b} z$ 
D)  $5 \log _{\mathrm{b}} \mathrm{yz}$ 
A)  $5 \log _{b} y+5 \log _{b} z$ 
B)  $\log _{b} y+\log _{b} 5 z$ 
C)  $\log _{b} y+5 \log _{b} z$ 
D)  $5 \log _{\mathrm{b}} \mathrm{yz}$

Question 5

For the given functions $f(x)$ and $g(x)$, find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated.
-$f(x)=x+4, g(x)=2 x-7$
Find $\left(\frac{f}{g}\right)(x)$.

Accepted Answer

A)  $\frac{2 x-7}{x+4}$ 
B)  $\frac{x}{2}-\frac{4}{7}$ 
C)  $\frac{x+4}{2 x-7}$ 
D)  $\frac{x}{2 x-7}+4$ 
A)  $\frac{2 x-7}{x+4}$ 
B)  $\frac{x}{2}-\frac{4}{7}$ 
C)  $\frac{x+4}{2 x-7}$ 
D)  $\frac{x}{2 x-7}+4$

Question 6

Rewrite in exponential form.
-$\log _{5} \frac{1}{25}=-2$

Accepted Answer

A)  $\left(\frac{1}{25}\right)^{2}=5$ 
B)  $5^{25}=2$ 
C)  $5^{-2}=\frac{1}{25}$ 
D)  $2^{5}=\frac{1}{25}$ 
A)  $\left(\frac{1}{25}\right)^{2}=5$ 
B)  $5^{25}=2$ 
C)  $5^{-2}=\frac{1}{25}$ 
D)  $2^{5}=\frac{1}{25}$

Question 7

Given $f(x)$ and $g(x)$, find the indicated composition and state its domain.
-$f(x)=x^{2}-6, g(x)=2 x+4$
Find $(f \circ g)(x)$.

Accepted Answer

A)  $4 x^{2}+16 x+16$, all real numbers 
B)  $4 x^{2}+8 x+10$, all real numbers 
C)  $2 x^{2}-8$, all real numbers 
D)  $4 x^{2}+16 x+10$, all real numbers 
A)  $4 x^{2}+16 x+16$, all real numbers 
B)  $4 x^{2}+8 x+10$, all real numbers 
C)  $2 x^{2}-8$, all real numbers 
D)  $4 x^{2}+16 x+10$, all real numbers

Question 8

Solve. Round to the nearest thousandth, if necessary
-$9^{3-x}=17$

Accepted Answer

A)  $\{3.776\}$ 
B)  $\{1.111\}$ 
C)  $\{-1.111\}$ 
D)  $\{1.711\}$ 
A)  $\{3.776\}$ 
B)  $\{1.111\}$ 
C)  $\{-1.111\}$ 
D)  $\{1.711\}$

Question 9

Given $f(x)$ and $g(x)$, find the indicated composition and state its domain.
-$f(x)=4 x^{2}+2 x+3, g(x)=2 x-8$
Find $(\mathrm{g} \circ \mathrm{f})(\mathrm{x})$.

Accepted Answer

A)  $4 x^{2}+4 x-2$, all real numbers 
B)  $4 x^{2}+2 x-5$, all real numbers 
C)  $8 x^{2}+4 x+14$, all real numbers 
D)  $8 x^{2}+4 x-2$, all real numbers 
A)  $4 x^{2}+4 x-2$, all real numbers 
B)  $4 x^{2}+2 x-5$, all real numbers 
C)  $8 x^{2}+4 x+14$, all real numbers 
D)  $8 x^{2}+4 x-2$, all real numbers

Question 10

Solve.
-$\log (3 \mathrm{x}-5)=1$

Accepted Answer

A)  $\{2\}$ 
B)  $\{-5\}$ 
C)  $\{-2\}$ 
D)  $\{5\}$ 
A)  $\{2\}$ 
B)  $\{-5\}$ 
C)  $\{-2\}$ 
D)  $\{5\}$

Question 11

Determine whether the functions $f(x)$ and $g(x)$ are inverse functions.
-$f(x)=6 x+4$

Accepted Answer

A)  $f 1(x)=\frac{x}{6}-4$ 
B)  $f^{-1}(x)=\frac{x+4}{6}$ 
C)  Not a one- to- one function 
D)  $\mathrm{f}^{-1}(\mathrm{x})=\frac{\mathrm{x}-4}{6}$ 
A)  $f 1(x)=\frac{x}{6}-4$ 
B)  $f^{-1}(x)=\frac{x+4}{6}$ 
C)  Not a one- to- one function 
D)  $\mathrm{f}^{-1}(\mathrm{x})=\frac{\mathrm{x}-4}{6}$

Question 12

Evaluate the given function
-$f(x)=73 x+2$ - 150, $f(2)$

Accepted Answer

A)  $5,764,951$ 
B)  $5,764,651$ 
C)  $5,764,801$ 
D)  117,499 
A)  $5,764,951$ 
B)  $5,764,651$ 
C)  $5,764,801$ 
D)  117,499

Question 13

For the given functions f(x) and g(x), find (f + g)(x) or (f - g)(x) as indicated
-$f(x)=-5 x^{2}-18 x, g(x)=-11 x^{2}-20 x+3$
Find $(f-g)(x)$.

Accepted Answer

A)  $6 x^{2}-38 x-3$ 
B)  $-16 x^{2}-38 x+3$ 
C)  $8 x^{2}-3$ 
D)  $6 x^{2}+2 x-3$ 
A)  $6 x^{2}-38 x-3$ 
B)  $-16 x^{2}-38 x+3$ 
C)  $8 x^{2}-3$ 
D)  $6 x^{2}+2 x-3$

Question 14

Rewrite using the power rule. Assume all variables represent positive real numbers.
-$2 \log _{b} q$

Accepted Answer

A)  $\log _{b} q^{2}$ 
B)  $\log _{b} 2 q$ 
C)  $2 \log _{b} q^{2}$ 
D)  $2 \log _{b} 2 q$ 
A)  $\log _{b} q^{2}$ 
B)  $\log _{b} 2 q$ 
C)  $2 \log _{b} q^{2}$ 
D)  $2 \log _{b} 2 q$

Question 15

Graph the given function $f(x)$. Label the vertical asymptote. State the domain and range of the function.
-$f(x)=\log _{5} x$

Accepted Answer

A)  Vertical Asymptote: $ x=0 $;
Domain: $ (0, \infty) $; Range: $ (-\infty, \infty) $
  
B)  Vertical Asymptote: $ y=0 $;
 Domain: $ (-\infty, \infty) $ : Range: $ (-\infty, 0) $
  
C)  Vertical Asymptote: $ x=0 $;
Domain: $ (0, \infty) $; Range: $ (-\infty, \infty) $
  
D)  Vertical Asymptote: $ \mathrm{y}=0 $;
 Domain: $ (-\infty, \infty) $; Range: $ (0, \infty) $
  
A)  Vertical Asymptote: $ x=0 $;
Domain: $ (0, \infty) $; Range: $ (-\infty, \infty) $
  
B)  Vertical Asymptote: $ y=0 $;
 Domain: $ (-\infty, \infty) $ : Range: $ (-\infty, 0) $
  
C)  Vertical Asymptote: $ x=0 $;
Domain: $ (0, \infty) $; Range: $ (-\infty, \infty) $
  
D)  Vertical Asymptote: $ \mathrm{y}=0 $;
 Domain: $ (-\infty, \infty) $; Range: $ (0, \infty) $

Question 16

Solve.
-$\log _{6}\left(x^{2}+3 x+19\right)=\log _{6}\left(x^{2}+x-29\right)$

Accepted Answer

A)  $\{-24\}$ 
B)  $\left\{\frac{10}{2}\right\}$ 
C)  $\varnothing$ 
D)  $\{-24,24\}$ 
A)  $\{-24\}$ 
B)  $\left\{\frac{10}{2}\right\}$ 
C)  $\varnothing$ 
D)  $\{-24,24\}$

Question 17

An element decays at the rate of $S(t)=\mathrm{se}^{-0.073 t}$, where $s$ is the initial amount in grams and $t$ is the time in years since this initial amount was present. If you have a 39-gram piece of this element, how many grams will you have 5 years from now? Round your answer to the nearest tenth of a gram.

Accepted Answer

A)  $27.1 \mathrm{~g}$ 
B)  $0.7 \mathrm{~g}$ 
C)  $56.2 \mathrm{~g}$ 
D)  $18.1 \mathrm{~g}$ 
A)  $27.1 \mathrm{~g}$ 
B)  $0.7 \mathrm{~g}$ 
C)  $56.2 \mathrm{~g}$ 
D)  $18.1 \mathrm{~g}$

Question 18

Compute the compound interest.
-Tony invested $\$ 2500$ at $9 \%$ compounded annually. How much will be in the account in 5 years? Round to the nearest cent.

Accepted Answer

A)  $\$ 1346.56$ 
B)  $\$ 2501.68$ 
C)  $\$ 3846.56$ 
D)  $\$ 2595.17$ 
A)  $\$ 1346.56$ 
B)  $\$ 2501.68$ 
C)  $\$ 3846.56$ 
D)  $\$ 2595.17$

Question 19

Find the specified domain
-For $f(x)=7 x-7$ and $g(x)=8 x+6$, what is the domain of $f \circ g$ ?

Accepted Answer

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

Question 20

Rew rite as a single logarithm. A ssume all variables represent positive real numbers.
-$6 \log (x+3)-4 \log \left(x^{2}+4\right)+\frac{1}{5} \log y$

Accepted Answer

A)  $\log \frac{(\mathrm{x}+3)^{6}\left(\mathrm{x}^{2}+4\right)^{4}}{\sqrt[5]{\mathrm{y}}}$ 
B)  $\frac{24}{5} \log \frac{(\mathrm{x}+3)\left(\mathrm{x}^{2}+4\right)}{\mathrm{y}}$ 
C)  $\log \frac{(x+3)^{6} \sqrt[5]{y}}{\left(x^{2}+4\right)^{4}}$ 
D)  $\frac{11}{5} \log \frac{(\mathrm{x}+3) \mathrm{y}}{\mathrm{x}^{2}+4}$ 
A)  $\log \frac{(\mathrm{x}+3)^{6}\left(\mathrm{x}^{2}+4\right)^{4}}{\sqrt[5]{\mathrm{y}}}$ 
B)  $\frac{24}{5} \log \frac{(\mathrm{x}+3)\left(\mathrm{x}^{2}+4\right)}{\mathrm{y}}$ 
C)  $\log \frac{(x+3)^{6} \sqrt[5]{y}}{\left(x^{2}+4\right)^{4}}$ 
D)  $\frac{11}{5} \log \frac{(\mathrm{x}+3) \mathrm{y}}{\mathrm{x}^{2}+4}$

Rewrite in exponential form. - $\log 100.01=-2$

Evaluate the given function. Round to the nearest thousandth. - $f(x)=e^{x}, f(1.3)$

Graph the given function f(x). Label the vertical asymptote. State the domain and range of the function. - $f(x)=\log _{1 / 4} x$ $Graph the given function f(x). Label the vertical asymptote. State the domain and range of the function. - f(x)=\log _{1 / 4} x$

Rewrite using the pow er and product rules. Assume all variables represent positive real numbers. - $\log _{\mathrm{b}} \mathrm{yz}^{5}$

For the given functions $f(x)$ and $g(x)$ , find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated. - $f(x)=x+4, g(x)=2 x-7$ Find $\left(\frac{f}{g}\right)(x)$ .

Rewrite in exponential form. - $\log _{5} \frac{1}{25}=-2$

Given $f(x)$ and $g(x)$ , find the indicated composition and state its domain. - $f(x)=x^{2}-6, g(x)=2 x+4$ Find $(f \circ g)(x)$ .

Solve. Round to the nearest thousandth, if necessary - $9^{3-x}=17$

Given $f(x)$ and $g(x)$ , find the indicated composition and state its domain. - $f(x)=4 x^{2}+2 x+3, g(x)=2 x-8$ Find $(\mathrm{g} \circ \mathrm{f})(\mathrm{x})$ .

Solve. - $\log (3 \mathrm{x}-5)=1$

Determine whether the functions $f(x)$ and $g(x)$ are inverse functions. - $f(x)=6 x+4$

Evaluate the given function - $f(x)=73 x+2$ - 150, $f(2)$

For the given functions f(x) and g(x), find (f + g)(x) or (f - g)(x) as indicated - $f(x)=-5 x^{2}-18 x, g(x)=-11 x^{2}-20 x+3$ Find $(f-g)(x)$ .

Rewrite using the power rule. Assume all variables represent positive real numbers. - $2 \log _{b} q$

Graph the given function $f(x)$ . Label the vertical asymptote. State the domain and range of the function. - $f(x)=\log _{5} x$ $Graph the given function f(x) . Label the vertical asymptote. State the domain and range of the function. - f(x)=\log _{5} x$

Solve. - $\log _{6}\left(x^{2}+3 x+19\right)=\log _{6}\left(x^{2}+x-29\right)$

Compute the compound interest. -Tony invested $\$ 2500$ at $9 \%$ compounded annually. How much will be in the account in 5 years? Round to the nearest cent.

Find the specified domain -For $f(x)=7 x-7$ and $g(x)=8 x+6$ , what is the domain of $f \circ g$ ?

Rew rite as a single logarithm. A ssume all variables represent positive real numbers. - $6 \log (x+3)-4 \log \left(x^{2}+4\right)+\frac{1}{5} \log y$

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

Rewrite in exponential form. - log⁡100.01=−2\log 100.01=-2log100.01=−2

Evaluate the given function. Round to the nearest thousandth. - f(x)=ex,f(1.3)f(x)=e^{x}, f(1.3)f(x)=ex,f(1.3)

Graph the given function f(x). Label the vertical asymptote. State the domain and range of the function. - f(x)=log⁡1/4xf(x)=\log _{1 / 4} xf(x)=log1/4​x

Rewrite using the pow er and product rules. Assume all variables represent positive real numbers. - log⁡byz5\log _{\mathrm{b}} \mathrm{yz}^{5}logb​yz5

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)=x+4,g(x)=2x−7f(x)=x+4, g(x)=2 x-7f(x)=x+4,g(x)=2x−7 Find (fg)(x)\left(\frac{f}{g}\right)(x)(gf​)(x) .

Rewrite in exponential form. - log⁡5125=−2\log _{5} \frac{1}{25}=-2log5​251​=−2

Given f(x)f(x)f(x) and g(x)g(x)g(x) , find the indicated composition and state its domain. - f(x)=x2−6,g(x)=2x+4f(x)=x^{2}-6, g(x)=2 x+4f(x)=x2−6,g(x)=2x+4 Find (f∘g)(x)(f \circ g)(x)(f∘g)(x) .

Solve. Round to the nearest thousandth, if necessary - 93−x=179^{3-x}=1793−x=17

Given f(x)f(x)f(x) and g(x)g(x)g(x) , find the indicated composition and state its domain. - f(x)=4x2+2x+3,g(x)=2x−8f(x)=4 x^{2}+2 x+3, g(x)=2 x-8f(x)=4x2+2x+3,g(x)=2x−8 Find (g∘f)(x)(\mathrm{g} \circ \mathrm{f})(\mathrm{x})(g∘f)(x) .

Solve. - log⁡(3x−5)=1\log (3 \mathrm{x}-5)=1log(3x−5)=1

Determine whether the functions f(x)f(x)f(x) and g(x)g(x)g(x) are inverse functions. - f(x)=6x+4f(x)=6 x+4f(x)=6x+4

Evaluate the given function - f(x)=73x+2f(x)=73 x+2f(x)=73x+2 - 150, f(2)f(2)f(2)

For the given functions f(x) and g(x), find (f + g)(x) or (f - g)(x) as indicated - f(x)=−5x2−18x,g(x)=−11x2−20x+3f(x)=-5 x^{2}-18 x, g(x)=-11 x^{2}-20 x+3f(x)=−5x2−18x,g(x)=−11x2−20x+3 Find (f−g)(x)(f-g)(x)(f−g)(x) .

Rewrite using the power rule. Assume all variables represent positive real numbers. - 2log⁡bq2 \log _{b} q2logb​q

Graph the given function f(x)f(x)f(x) . Label the vertical asymptote. State the domain and range of the function. - f(x)=log⁡5xf(x)=\log _{5} xf(x)=log5​x

Solve. - log⁡6(x2+3x+19)=log⁡6(x2+x−29)\log _{6}\left(x^{2}+3 x+19\right)=\log _{6}\left(x^{2}+x-29\right)log6​(x2+3x+19)=log6​(x2+x−29)

Compute the compound interest. -Tony invested $2500\$ 2500$2500 at 9%9 \%9% compounded annually. How much will be in the account in 5 years? Round to the nearest cent.

Find the specified domain -For f(x)=7x−7f(x)=7 x-7f(x)=7x−7 and g(x)=8x+6g(x)=8 x+6g(x)=8x+6 , what is the domain of f∘gf \circ gf∘g ?

Rew rite as a single logarithm. A ssume all variables represent positive real numbers. - 6log⁡(x+3)−4log⁡(x2+4)+15log⁡y6 \log (x+3)-4 \log \left(x^{2}+4\right)+\frac{1}{5} \log y6log(x+3)−4log(x2+4)+51​logy