Question 1

Expand. A ssume that all variables represent positive real numbers.
-$\log _{d}\left(\frac{a^{8} b^{2}}{c^{6} d^{3}}\right)$

Accepted Answer

A)  $8 \log _{d} a+2 \log _{d} b-6 \log _{d} c+3$ 
B)  $a^{8} b^{2}-c^{6} d^{3}$ 
C)  $\log _{d} a^{8}+\log _{d} b^{2}+\log _{d} c^{6}-\log _{d} b^{3}$ 
D)  $8 \log _{d} a+2 \log _{d} b-6 \log _{d} c-3$ 
A)  $8 \log _{d} a+2 \log _{d} b-6 \log _{d} c+3$ 
B)  $a^{8} b^{2}-c^{6} d^{3}$ 
C)  $\log _{d} a^{8}+\log _{d} b^{2}+\log _{d} c^{6}-\log _{d} b^{3}$ 
D)  $8 \log _{d} a+2 \log _{d} b-6 \log _{d} c-3$

Question 2

Solve. Round to the nearest thousandth, if necessary
-$3^{-4 \mathrm{x}-1}=18$

Accepted Answer

A)  $\{-0.698\}$ 
B)  $\{1.75\}$ 
C)  $\{0.408\}$ 
D)  $\{0.908\}$ 
A)  $\{-0.698\}$ 
B)  $\{1.75\}$ 
C)  $\{0.408\}$ 
D)  $\{0.908\}$

Question 3

Use the horizontal-line test to determine whether the function is one to one.
-

Accepted Answer

A) True 
 B)False

Question 4

Solve the equation.
-$\log (2+\mathrm{x})-\log (\mathrm{x}-5)=\log 2$

Accepted Answer

A)  $\{-12\}$ 
B)  $\{12\}$ 
C)  $\varnothing$ 
D)  $\left\{\frac{5}{2}\right\}$ 
A)  $\{-12\}$ 
B)  $\{12\}$ 
C)  $\varnothing$ 
D)  $\left\{\frac{5}{2}\right\}$

Question 5

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

Accepted Answer

A)  $-8 x+36$, all real numbers 
B)  $-8 x+16$, all real numbers 
C)  $x+16$, all real numbers 
D)  - $8 x-0$, all real numbers 
A)  $-8 x+36$, all real numbers 
B)  $-8 x+16$, all real numbers 
C)  $x+16$, all real numbers 
D)  - $8 x-0$, all real numbers

Question 6

Solve the equation.
-$\log (x+3)=1-\log x$

Accepted Answer

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

Question 7

For the given functions $f(x)$ and $g(x)$, find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated.
-$f(x)=x^{2}+8 x+12, g(x)=x+6$
Find $\left(\frac{f}{g}\right)(x)$.

Accepted Answer

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

Question 8

Find the specified domain
-For $f(x)=\frac{6}{x^{2}}$ and $g(x)=4-x$, what is the domain of $f \circ g$ ?

Accepted Answer

A)  $(-\infty, 4) \cup(4, \infty)$ 
B)  $(-\infty, 0) \cup(0, \infty)$ 
C)  $(-\infty, 0) \cup(0,4) \cup(4, \infty)$ 
D)  $(-\infty, \infty)$ 
A)  $(-\infty, 4) \cup(4, \infty)$ 
B)  $(-\infty, 0) \cup(0, \infty)$ 
C)  $(-\infty, 0) \cup(0,4) \cup(4, \infty)$ 
D)  $(-\infty, \infty)$

Question 9

Determine whether the functions $f(x)$ and $g(x)$ are inverse functions.
-$f(x)=x-9, g(x)=x+9$

Accepted Answer

A) True 
 B)False

Question 10

Graph the given function f(x). Label the vertical asymptote. State the domain and range of the function.
-Let $\mathrm{f}(\mathrm{x})=\ln (\mathrm{x}-5)+15$.. Solve $\mathrm{f}(\mathrm{x})=15$.

Accepted Answer

A)  $\{20\}$ 
B)  $\{10\}$ 
C)  $\{-4\}$ 
D)  $\{6\}$ 
A)  $\{20\}$ 
B)  $\{10\}$ 
C)  $\{-4\}$ 
D)  $\{6\}$

Question 11

Evaluate the given function. Round to the nearest thousandth.
-$f(x)=e^{x+2}, f(-1)$

Accepted Answer

A)  2.718 
B)  2.368 
C)  6.389 
D)  3.718 
A)  2.718 
B)  2.368 
C)  6.389 
D)  3.718

Question 12

Determine the equation of the vertical asymptote for the graph of this function, and state the domain and range of this function.
-$f(x)=\log (x+4)-4$

Accepted Answer

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

Question 13

Rewrite in terms of two or more logarithms using the quotient and product rules for logarithms. Assume all variables represent positive real numbers.
-$\log _{\mathrm{w}}\left(\frac{7 \mathrm{x}}{4}\right)$

Accepted Answer

A)  $\log _{\mathrm{w}} 7+\log _{\mathrm{W}} \mathrm{x}-\log _{\mathrm{W}} 4$ 
B)  $\log _{\mathrm{W}} 7+\log _{\mathrm{w}} \mathrm{x}+\log _{\mathrm{W}} 4$ 
C)  $\log _{w} 7 x-\log _{w} 4$ 
D)  $\log _{w} 3 x$ 
A)  $\log _{\mathrm{w}} 7+\log _{\mathrm{W}} \mathrm{x}-\log _{\mathrm{W}} 4$ 
B)  $\log _{\mathrm{W}} 7+\log _{\mathrm{w}} \mathrm{x}+\log _{\mathrm{W}} 4$ 
C)  $\log _{w} 7 x-\log _{w} 4$ 
D)  $\log _{w} 3 x$

Question 14

Rew rite as a single logarithm. A ssume all variables represent positive real numbers.
-$\log _{b} x^{8}-2 \log _{b} \sqrt{x}$

Accepted Answer

A)  $\log _{b} x^{7}$ 
B)  $\frac{\log _{b} x^{8}}{\log _{b} x}$ 
C)  $\log _{b}\left(x^{8}-x\right)$ 
D)  $\log _{b} x^{9}$ 
A)  $\log _{b} x^{7}$ 
B)  $\frac{\log _{b} x^{8}}{\log _{b} x}$ 
C)  $\log _{b}\left(x^{8}-x\right)$ 
D)  $\log _{b} x^{9}$

Question 15

Solve the problem.
-Find $(f+g)(4)$ when $f(x)=x+7$ and $g(x)=x+1$.

Accepted Answer

A)  0 
B)  14 
C)  16 
D)  2 
A)  0 
B)  14 
C)  16 
D)  2

Question 16

Determine whether the functions $f(x)$ and $g(x)$ are inverse functions.
-$f(x)=-x+9, g(x)=x-9$

Accepted Answer

A) True 
 B)False

Question 17

Solve the equation.
-$\log x+\log (x+1)=\log 2$

Accepted Answer

A)  $\left\{\frac{3}{2}\right\}$ 
B)  $\{-1,2\}$ 
C)  $\{2\}$ 
D)  $\{1\}$ 
A)  $\left\{\frac{3}{2}\right\}$ 
B)  $\{-1,2\}$ 
C)  $\{2\}$ 
D)  $\{1\}$

Question 18

Graph f(x). State the domain, range, and horizontal asymptote of the function
-$f(x)=2^{x}$

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

Question 19

The decay of $200 \mathrm{mg}$ of an isotope is given by $\mathrm{A}(\mathrm{t})=200 \mathrm{e}^{-0.012 \mathrm{t}}$, where $t$ is time in years since the initial amount of $200 \mathrm{mg}$ was present. Find the amount left (to the nearest $\mathrm{mg}$ ) after 71 years.

Accepted Answer

A)  $84 \mathrm{mg}$ 
B)  $43 \mathrm{mg}$ 
C)  $198 \mathrm{mg}$ 
D)  $85 \mathrm{mg}$ 
A)  $84 \mathrm{mg}$ 
B)  $43 \mathrm{mg}$ 
C)  $198 \mathrm{mg}$ 
D)  $85 \mathrm{mg}$

Question 20

Rewrite in logarithmic form
-$4^{-2}=\frac{1}{16}$

Accepted Answer

A)  $\log _{4}-2=\frac{1}{16}$ 
B)  $\log _{-2} \frac{1}{16}=4$ 
C)  $\log _{4} \frac{1}{16}=-2$ 
D)  $\log _{1 / 16} 4=-2$ 
A)  $\log _{4}-2=\frac{1}{16}$ 
B)  $\log _{-2} \frac{1}{16}=4$ 
C)  $\log _{4} \frac{1}{16}=-2$ 
D)  $\log _{1 / 16} 4=-2$

Expand. A ssume that all variables represent positive real numbers. - $\log _{d}\left(\frac{a^{8} b^{2}}{c^{6} d^{3}}\right)$

Solve. Round to the nearest thousandth, if necessary - $3^{-4 \mathrm{x}-1}=18$

Use the horizontal-line test to determine whether the function is one to one. -

Solve the equation. - $\log (2+\mathrm{x})-\log (\mathrm{x}-5)=\log 2$

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

Solve the equation. - $\log (x+3)=1-\log x$

For the given functions $f(x)$ and $g(x)$ , find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated. - $f(x)=x^{2}+8 x+12, g(x)=x+6$ Find $\left(\frac{f}{g}\right)(x)$ .

Find the specified domain -For $f(x)=\frac{6}{x^{2}}$ and $g(x)=4-x$ , what is the domain of $f \circ g$ ?

Determine whether the functions $f(x)$ and $g(x)$ are inverse functions. - $f(x)=x-9, g(x)=x+9$

Graph the given function f(x). Label the vertical asymptote. State the domain and range of the function. -Let $\mathrm{f}(\mathrm{x})=\ln (\mathrm{x}-5)+15$ .. Solve $\mathrm{f}(\mathrm{x})=15$ .

Evaluate the given function. Round to the nearest thousandth. - $f(x)=e^{x+2}, f(-1)$

Determine the equation of the vertical asymptote for the graph of this function, and state the domain and range of this function. - $f(x)=\log (x+4)-4$

Rewrite in terms of two or more logarithms using the quotient and product rules for logarithms. Assume all variables represent positive real numbers. - $\log _{\mathrm{w}}\left(\frac{7 \mathrm{x}}{4}\right)$

Rew rite as a single logarithm. A ssume all variables represent positive real numbers. - $\log _{b} x^{8}-2 \log _{b} \sqrt{x}$

Solve the problem. -Find $(f+g)(4)$ when $f(x)=x+7$ and $g(x)=x+1$ .

Determine whether the functions $f(x)$ and $g(x)$ are inverse functions. - $f(x)=-x+9, g(x)=x-9$

Solve the equation. - $\log x+\log (x+1)=\log 2$

Graph f(x). State the domain, range, and horizontal asymptote of the function - $f(x)=2^{x}$ $Graph f(x). State the domain, range, and horizontal asymptote of the function - f(x)=2^{x}$

The decay of $200 \mathrm{mg}$ of an isotope is given by $\mathrm{A}(\mathrm{t})=200 \mathrm{e}^{-0.012 \mathrm{t}}$ , where $t$ is time in years since the initial amount of $200 \mathrm{mg}$ was present. Find the amount left (to the nearest $\mathrm{mg}$ ) after 71 years.

Rewrite in logarithmic form - $4^{-2}=\frac{1}{16}$

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

Expand. A ssume that all variables represent positive real numbers. - log⁡d(a8b2c6d3)\log _{d}\left(\frac{a^{8} b^{2}}{c^{6} d^{3}}\right)logd​(c6d3a8b2​)

Solve. Round to the nearest thousandth, if necessary - 3−4x−1=183^{-4 \mathrm{x}-1}=183−4x−1=18

Use the horizontal-line test to determine whether the function is one to one. -

Solve the equation. - log⁡(2+x)−log⁡(x−5)=log⁡2\log (2+\mathrm{x})-\log (\mathrm{x}-5)=\log 2log(2+x)−log(x−5)=log2

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

Solve the equation. - log⁡(x+3)=1−log⁡x\log (x+3)=1-\log xlog(x+3)=1−logx

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)=x2+8x+12,g(x)=x+6f(x)=x^{2}+8 x+12, g(x)=x+6f(x)=x2+8x+12,g(x)=x+6 Find (fg)(x)\left(\frac{f}{g}\right)(x)(gf​)(x) .

Find the specified domain -For f(x)=6x2f(x)=\frac{6}{x^{2}}f(x)=x26​ and g(x)=4−xg(x)=4-xg(x)=4−x , what is the domain of f∘gf \circ gf∘g ?

Determine whether the functions f(x)f(x)f(x) and g(x)g(x)g(x) are inverse functions. - f(x)=x−9,g(x)=x+9f(x)=x-9, g(x)=x+9f(x)=x−9,g(x)=x+9

Graph the given function f(x). Label the vertical asymptote. State the domain and range of the function. -Let f(x)=ln⁡(x−5)+15\mathrm{f}(\mathrm{x})=\ln (\mathrm{x}-5)+15f(x)=ln(x−5)+15 .. Solve f(x)=15\mathrm{f}(\mathrm{x})=15f(x)=15 .

Evaluate the given function. Round to the nearest thousandth. - f(x)=ex+2,f(−1)f(x)=e^{x+2}, f(-1)f(x)=ex+2,f(−1)

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⁡(x+4)−4f(x)=\log (x+4)-4f(x)=log(x+4)−4

Rewrite in terms of two or more logarithms using the quotient and product rules for logarithms. Assume all variables represent positive real numbers. - log⁡w(7x4)\log _{\mathrm{w}}\left(\frac{7 \mathrm{x}}{4}\right)logw​(47x​)

Rew rite as a single logarithm. A ssume all variables represent positive real numbers. - log⁡bx8−2log⁡bx\log _{b} x^{8}-2 \log _{b} \sqrt{x}logb​x8−2logb​x​

Solve the problem. -Find (f+g)(4)(f+g)(4)(f+g)(4) when f(x)=x+7f(x)=x+7f(x)=x+7 and g(x)=x+1g(x)=x+1g(x)=x+1 .

Determine whether the functions f(x)f(x)f(x) and g(x)g(x)g(x) are inverse functions. - f(x)=−x+9,g(x)=x−9f(x)=-x+9, g(x)=x-9f(x)=−x+9,g(x)=x−9

Solve the equation. - log⁡x+log⁡(x+1)=log⁡2\log x+\log (x+1)=\log 2logx+log(x+1)=log2

Graph f(x). State the domain, range, and horizontal asymptote of the function - f(x)=2xf(x)=2^{x}f(x)=2x

Rewrite in logarithmic form - 4−2=1164^{-2}=\frac{1}{16}4−2=161​

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

Expand. A ssume that all variables represent positive real numbers. - $\log _{d}\left(\frac{a^{8} b^{2}}{c^{6} d^{3}}\right)$

Solve. Round to the nearest thousandth, if necessary - $3^{-4 \mathrm{x}-1}=18$

Solve the equation. - $\log (2+\mathrm{x})-\log (\mathrm{x}-5)=\log 2$

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

Solve the equation. - $\log (x+3)=1-\log x$

For the given functions $f(x)$ and $g(x)$ , find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated. - $f(x)=x^{2}+8 x+12, g(x)=x+6$ Find $\left(\frac{f}{g}\right)(x)$ .

Find the specified domain -For $f(x)=\frac{6}{x^{2}}$ and $g(x)=4-x$ , what is the domain of $f \circ g$ ?

Determine whether the functions $f(x)$ and $g(x)$ are inverse functions. - $f(x)=x-9, g(x)=x+9$

Graph the given function f(x). Label the vertical asymptote. State the domain and range of the function. -Let $\mathrm{f}(\mathrm{x})=\ln (\mathrm{x}-5)+15$ .. Solve $\mathrm{f}(\mathrm{x})=15$ .

Evaluate the given function. Round to the nearest thousandth. - $f(x)=e^{x+2}, f(-1)$

Determine the equation of the vertical asymptote for the graph of this function, and state the domain and range of this function. - $f(x)=\log (x+4)-4$

Rewrite in terms of two or more logarithms using the quotient and product rules for logarithms. Assume all variables represent positive real numbers. - $\log _{\mathrm{w}}\left(\frac{7 \mathrm{x}}{4}\right)$

Rew rite as a single logarithm. A ssume all variables represent positive real numbers. - $\log _{b} x^{8}-2 \log _{b} \sqrt{x}$

Solve the problem. -Find $(f+g)(4)$ when $f(x)=x+7$ and $g(x)=x+1$ .

Determine whether the functions $f(x)$ and $g(x)$ are inverse functions. - $f(x)=-x+9, g(x)=x-9$

Solve the equation. - $\log x+\log (x+1)=\log 2$

Graph f(x). State the domain, range, and horizontal asymptote of the function - $f(x)=2^{x}$ $Graph f(x). State the domain, range, and horizontal asymptote of the function - f(x)=2^{x}$

Rewrite in logarithmic form - $4^{-2}=\frac{1}{16}$