Question 1

Solve the problem.
-Find $(f+g)(-2)$ when $f(x)=-2 x^{3}-3 x-35$ and $g(x)=5 x^{2}+2 x$

Accepted Answer

A)  3 
B)  -7 
C)  -27 
D)  -9 
A)  3 
B)  -7 
C)  -27 
D)  -9

Question 2

Evaluate.
-$\log _{6}\left(\frac{1}{36}\right)$

Accepted Answer

A)  2 
B)  6 
C)  -6 
D)  - 2 
A)  2 
B)  6 
C)  -6 
D)  - 2

Question 3

Simplify.
-$2^{\log _{2} \mathrm{x}}$

Accepted Answer

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

Question 4

Solve.
-$2 \mathrm{x}=16$

Accepted Answer

A)  $\{5\}$ 
B)  $\{4\}$ 
C)  $\{3\}$ 
D)  $\{-4\}$. 
A)  $\{5\}$ 
B)  $\{4\}$ 
C)  $\{3\}$ 
D)  $\{-4\}$.

Question 5

Given $f(x)$ and $g(x)$, find the indicated composition and evaluate.
-$f(x)=7 x+9 ; g(x)=5 x+5$
Find $(\mathrm{f} \circ \mathrm{g})(4)$.

Accepted Answer

A)  190 
B)  62 
C)  184 
D)  925 
A)  190 
B)  62 
C)  184 
D)  925

Question 6

Compute the compound interest.
-Binal Patel invested $\$ 5500$ at $9 \%$ compounded semiannually. How much will be in the account in 8 years? Round to the nearest cent.

Accepted Answer

A)  $\$ 11,123.04$ 
B)  $\$ 7821.55$ 
C)  $\$ 21,836.68$ 
D)  $\$ 10,959.09$ 
A)  $\$ 11,123.04$ 
B)  $\$ 7821.55$ 
C)  $\$ 21,836.68$ 
D)  $\$ 10,959.09$

Question 7

Expand. A ssume that all variables represent positive real numbers.
-$\log _{4}\left(\frac{\sqrt{\mathrm{x}}}{64}\right)$

Accepted Answer

A)  $\frac{1}{2} \log _{4} x-\log _{4} 64$ 
B)  $\log _{4} \sqrt{x}-\log _{4} 64$ 
C)  $\log _{4} \sqrt{x}-3 \log _{4} 4$ 
D)  $\frac{1}{2} \log _{4} \mathrm{x}-3$ 
A)  $\frac{1}{2} \log _{4} x-\log _{4} 64$ 
B)  $\log _{4} \sqrt{x}-\log _{4} 64$ 
C)  $\log _{4} \sqrt{x}-3 \log _{4} 4$ 
D)  $\frac{1}{2} \log _{4} \mathrm{x}-3$

Question 8

Solve the problem.
-The population growth of an animal species is described by $F(t)=500+80 \log 3(2 t+1)$, where $t$ is measured in months. Find the population of this species in an area 4 month(s) after the species is introduced.

Accepted Answer

A)  1220 
B)  630 
C)  660 
D)  340 
A)  1220 
B)  630 
C)  660 
D)  340

Question 9

For the given functions $f(x)$ and $g(x)$, find a value $x$ for which $(f\circ g)(x)=(g\circ f)(x)$.
-$f(x)=x^{2}+9 x+7, g(x)=x+2$

Accepted Answer

A)  $x=-\frac{5}{2}$ 
B)  $x=5$ 
C)  $x=-5$ 
D)  $\mathrm{x}=2$ 
A)  $x=-\frac{5}{2}$ 
B)  $x=5$ 
C)  $x=-5$ 
D)  $\mathrm{x}=2$

Question 10

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 11

Evaluate. Round to the nearest thousandth, if necessary.
-$\log 3.20$

Accepted Answer

A)  1.163 
B)  0.519 
C)  0.505 
D)  0.491 
A)  1.163 
B)  0.519 
C)  0.505 
D)  0.491

Question 12

Rewrite as a single logarithm using the product rule for logarithms. A ssume all variables represent positive real numbers.
-$\log _{6} 9+\log _{6} 9$

Accepted Answer

A)  $\log _{12} 18$ 
B)  $\log _{6} 81$ 
C)  $\log _{6} 18$ 
D)  $\log _{12} 81$ 
A)  $\log _{12} 18$ 
B)  $\log _{6} 81$ 
C)  $\log _{6} 18$ 
D)  $\log _{12} 81$

Question 13

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

Accepted Answer

A)  Vertical asymptote: $x=0$;
Domain: $(0, \infty)$, Range: $(-\infty, \infty)$ 
B)  Vertical asymptote: $\mathrm{x}=0$;
Domain: $(-\infty, 0)$, Range: $(-\infty, \infty)$ 
C)  Vertical asymptote: $\mathrm{x}=-2$;
Domain: $(-2, \infty)$, Range: $(-\infty, \infty)$ 
D)  Vertical asymptote: $\mathrm{x}=5$;
Domain: $(5, \infty)$, Range: $(-\infty, \infty)$ 
A)  Vertical asymptote: $x=0$;
Domain: $(0, \infty)$, Range: $(-\infty, \infty)$ 
B)  Vertical asymptote: $\mathrm{x}=0$;
Domain: $(-\infty, 0)$, Range: $(-\infty, \infty)$ 
C)  Vertical asymptote: $\mathrm{x}=-2$;
Domain: $(-2, \infty)$, Range: $(-\infty, \infty)$ 
D)  Vertical asymptote: $\mathrm{x}=5$;
Domain: $(5, \infty)$, Range: $(-\infty, \infty)$

Question 14

Solve. Round to the nearest thousandth.
-$\mathrm{e}^{2 \mathrm{x}}+14 \mathrm{e}^{\mathrm{x}}-51=0$

Accepted Answer

A)  $\{2.833\}$ 
B)  $\{1.738\}$ 
C)  $\{1.099\}$ 
D)  $\{1.099,2.833\}$ 
A)  $\{2.833\}$ 
B)  $\{1.738\}$ 
C)  $\{1.099\}$ 
D)  $\{1.099,2.833\}$

Question 15

Find the specified domain
-For $f(x)=\frac{1}{x-2}$ and $g(x)=\frac{7}{x}$, what is the domain of $g \circ f$ ?

Accepted Answer

A)  $(-\infty, 0) \cup\left(0, \frac{7}{2}\right) \cup\left(\frac{7}{2}, \infty\right)$ 
B)  $(-\infty, 2) \cup(2, \infty)$ 
C)  $(-\infty, 0) \cup(0, \infty)$ 
D)  $(-\infty, 0) \cup(0,2) \cup(2, \infty)$ 
A)  $(-\infty, 0) \cup\left(0, \frac{7}{2}\right) \cup\left(\frac{7}{2}, \infty\right)$ 
B)  $(-\infty, 2) \cup(2, \infty)$ 
C)  $(-\infty, 0) \cup(0, \infty)$ 
D)  $(-\infty, 0) \cup(0,2) \cup(2, \infty)$

Question 16

Solve.
-$4^{1+2 x}=1024$

Accepted Answer

A)  $\{8\}$ 
B)  $\{256\}$ 
C)  $\{-2\}$ 
D)  $\{2\}$ 
A)  $\{8\}$ 
B)  $\{256\}$ 
C)  $\{-2\}$ 
D)  $\{2\}$

Question 17

Solve.
-$4^{19 x}+171=1$

Accepted Answer

A)  $\{9\}$ 
B)  $\{0\}$ 
C)  $\{-9\}$ 
D)  $\{1\}$ 
A)  $\{9\}$ 
B)  $\{0\}$ 
C)  $\{-9\}$ 
D)  $\{1\}$

Question 18

Solve.
-$\log 3\left(\frac{\mathrm{x}-1}{10 \mathrm{x}-8}\right)=-2$

Accepted Answer

A)  $\{-1\}$ 
B)  $\varnothing$ 
C)  $\{17\}$ 
D)  $\{-9,9\}$ 
A)  $\{-1\}$ 
B)  $\varnothing$ 
C)  $\{17\}$ 
D)  $\{-9,9\}$

Question 19

For the given function $f(x)$, find $f^{-1}(x)$. State the domain of $f^{-1}(x)$.
-$f(x)=\sqrt{x-1}+7$

Accepted Answer

A)  $f 1(x)=(x-7)^{2}+1, x \geq 7$ 
B)  $f^{-1}(x)=(x+1)^{2}-7, x \geq-1$ 
C)  $f^{1}(x)=x^{2}+7, x \geq 0$ 
D)  $f^{-1}(x)=(x+7)^{2}-1, x \geq-7$ 
A)  $f 1(x)=(x-7)^{2}+1, x \geq 7$ 
B)  $f^{-1}(x)=(x+1)^{2}-7, x \geq-1$ 
C)  $f^{1}(x)=x^{2}+7, x \geq 0$ 
D)  $f^{-1}(x)=(x+7)^{2}-1, x \geq-7$

Question 20

Compute the average rate of change for the logarithmic function on the given interval. Write your answer as a simplified fraction unless stated otherw ise.
-$f(x)=\log 2 x,[4,32]$

Accepted Answer

A)  $\frac{1}{14}$ 
B)  $\frac{7}{36}$ 
C)  $\frac{1}{4}$ 
D)  $\frac{3}{28}$ 
A)  $\frac{1}{14}$ 
B)  $\frac{7}{36}$ 
C)  $\frac{1}{4}$ 
D)  $\frac{3}{28}$

Solve the problem. -Find $(f+g)(-2)$ when $f(x)=-2 x^{3}-3 x-35$ and $g(x)=5 x^{2}+2 x$

Evaluate. - $\log _{6}\left(\frac{1}{36}\right)$

Simplify. - $2^{\log _{2} \mathrm{x}}$

Solve. - $2 \mathrm{x}=16$

Given $f(x)$ and $g(x)$ , find the indicated composition and evaluate. - $f(x)=7 x+9 ; g(x)=5 x+5$ Find $(\mathrm{f} \circ \mathrm{g})(4)$ .

Compute the compound interest. -Binal Patel invested $\$ 5500$ at $9 \%$ compounded semiannually. How much will be in the account in 8 years? Round to the nearest cent.

Expand. A ssume that all variables represent positive real numbers. - $\log _{4}\left(\frac{\sqrt{\mathrm{x}}}{64}\right)$

Solve the problem. -The population growth of an animal species is described by $F(t)=500+80 \log 3(2 t+1)$ , where $t$ is measured in months. Find the population of this species in an area 4 month(s) after the species is introduced.

For the given functions $f(x)$ and $g(x)$ , find a value $x$ for which $(f\circ g)(x)=(g\circ f)(x)$ . - $f(x)=x^{2}+9 x+7, g(x)=x+2$

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

Evaluate. Round to the nearest thousandth, if necessary. - $\log 3.20$

Rewrite as a single logarithm using the product rule for logarithms. A ssume all variables represent positive real numbers. - $\log _{6} 9+\log _{6} 9$

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

Solve. Round to the nearest thousandth. - $\mathrm{e}^{2 \mathrm{x}}+14 \mathrm{e}^{\mathrm{x}}-51=0$

Find the specified domain -For $f(x)=\frac{1}{x-2}$ and $g(x)=\frac{7}{x}$ , what is the domain of $g \circ f$ ?

Solve. - $4^{1+2 x}=1024$

Solve. - $4^{19 x}+171=1$

Solve. - $\log 3\left(\frac{\mathrm{x}-1}{10 \mathrm{x}-8}\right)=-2$

For the given function $f(x)$ , find $f^{-1}(x)$ . State the domain of $f^{-1}(x)$ . - $f(x)=\sqrt{x-1}+7$

Compute the average rate of change for the logarithmic function on the given interval. Write your answer as a simplified fraction unless stated otherw ise. - $f(x)=\log 2 x,[4,32]$

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 the problem. -Find (f+g)(−2)(f+g)(-2)(f+g)(−2) when f(x)=−2x3−3x−35f(x)=-2 x^{3}-3 x-35f(x)=−2x3−3x−35 and g(x)=5x2+2xg(x)=5 x^{2}+2 xg(x)=5x2+2x

Evaluate. - log⁡6(136)\log _{6}\left(\frac{1}{36}\right)log6​(361​)

Simplify. - 2log⁡2x2^{\log _{2} \mathrm{x}}2log2​x

Solve. - 2x=162 \mathrm{x}=162x=16

Given f(x)f(x)f(x) and g(x)g(x)g(x) , find the indicated composition and evaluate. - f(x)=7x+9;g(x)=5x+5f(x)=7 x+9 ; g(x)=5 x+5f(x)=7x+9;g(x)=5x+5 Find (f∘g)(4)(\mathrm{f} \circ \mathrm{g})(4)(f∘g)(4) .

Compute the compound interest. -Binal Patel invested $5500\$ 5500$5500 at 9%9 \%9% compounded semiannually. How much will be in the account in 8 years? Round to the nearest cent.

Expand. A ssume that all variables represent positive real numbers. - log⁡4(x64)\log _{4}\left(\frac{\sqrt{\mathrm{x}}}{64}\right)log4​(64x​​)

Solve the problem. -The population growth of an animal species is described by F(t)=500+80log⁡3(2t+1)F(t)=500+80 \log 3(2 t+1)F(t)=500+80log3(2t+1) , where ttt is measured in months. Find the population of this species in an area 4 month(s) after the species is introduced.

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)=x2+9x+7,g(x)=x+2f(x)=x^{2}+9 x+7, g(x)=x+2f(x)=x2+9x+7,g(x)=x+2