Question 1

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

Accepted Answer

A) True 
 B)False  True

Question 2

Given $f(x)$ and $g(x)$, find the indicated composition and state its domain.
-$f(x)=6 x+5, g(x)=4 x-1$
Find $(\mathrm{f} \circ \mathrm{g})(\mathrm{x})$.

Accepted Answer

A)  $24 x+4$, all real numbers 
B)  $24 x+19$, all real numbers 
C)  $24 x+11$, all real numbers 
D)  $24 \mathrm{x}-1$, all real numbers 
A)  $24 x+4$, all real numbers 
B)  $24 x+19$, all real numbers 
C)  $24 x+11$, all real numbers 
D)  $24 \mathrm{x}-1$, all real numbers D

Question 3

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) 
  A

Question 4

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

Accepted Answer

A)  $f-1(x)=x^{2}-4, x \geq 0$ 
B)  $f^{-1}(x)=-x^{2}+2, x \geq 0$ 
C)  $f^{1}(x)=\sqrt{x-2}, x \geq 2$ 
D)  $f^{-1}(x)=x^{2}-2, x \geq 0$ 
A)  $f-1(x)=x^{2}-4, x \geq 0$ 
B)  $f^{-1}(x)=-x^{2}+2, x \geq 0$ 
C)  $f^{1}(x)=\sqrt{x-2}, x \geq 2$ 
D)  $f^{-1}(x)=x^{2}-2, x \geq 0$

Question 5

Solve the problem.
-A certain country's population $\mathrm{P}(\mathrm{t})$, in millions, tyears after 2010 can be approximated by $\mathrm{P}(\mathrm{t})=3.495(1.018)^{\mathrm{t}}$.
Find the doubling time. Round your answer to the nearest tenth.

Accepted Answer

A)  $38.9 \mathrm{yr}$ 
B)  $61.6 \mathrm{yr}$ 
C)  $77.7 \mathrm{yr}$ 
D)  $70.1 \mathrm{yr}$ 
A)  $38.9 \mathrm{yr}$ 
B)  $61.6 \mathrm{yr}$ 
C)  $77.7 \mathrm{yr}$ 
D)  $70.1 \mathrm{yr}$

Question 6

The population growth of an animal species is described by $F(t)=700+90 \log 3(2 t+1)$ where $t$ is the number of months since the species was introduced. Find the population of this species in an area 4 month(s) after the species is introduced.

Accepted Answer

A)  450 
B)  775 
C)  880 
D)  1510 
A)  450 
B)  775 
C)  880 
D)  1510

Question 7

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

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: $ (-4, \infty) $, range: $ (-\infty, \infty) $
Vertical asymptote: $ x=-4 $ 
  
D)  Domain: $ (4, \infty) $, range: $ (-\infty, \infty) $ 
Vertical asymptote: $ x=4 $
  
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: $ (-4, \infty) $, range: $ (-\infty, \infty) $
Vertical asymptote: $ x=-4 $ 
  
D)  Domain: $ (4, \infty) $, range: $ (-\infty, \infty) $ 
Vertical asymptote: $ x=4 $

Question 8

For the given functions $f(x)$ and $g(x)$, find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated.
-$f(x)=-9 x+4, g(x)=5 x^{2}-x+4$
Find $(\mathrm{f} \cdot \mathrm{g})(\mathrm{x})$.

Accepted Answer

A)  $-45 x^{3}-40 x+16$ 
B)  $-45 x^{3}+11 x^{2}-40 x+16$ 
C)  $14 x^{2}-40 x+16$ 
D)  $-45 x^{3}+29 x^{2}-40 x+16$ 
A)  $-45 x^{3}-40 x+16$ 
B)  $-45 x^{3}+11 x^{2}-40 x+16$ 
C)  $14 x^{2}-40 x+16$ 
D)  $-45 x^{3}+29 x^{2}-40 x+16$

Question 9

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 10

Given $f(x)$ and $g(x)$, find the indicated composition and evaluate.
-$f(x)=6 x+2 ; g(x)=x+7$
Find $(f \circ g)(4)$.

Accepted Answer

A)  68 
B)  37 
C)  33 
D)  286 
A)  68 
B)  37 
C)  33 
D)  286

Question 11

Evaluate. Round to the nearest thousandth, if necessary.
-$\log 100,000$

Accepted Answer

A)  5 
B)  6 
C)  4 
D)  -5 
A)  5 
B)  6 
C)  4 
D)  -5

Question 12

Find all intercepts for the given function. Round to the nearest tenth if necessary.
-$f(x)=\log (x+9)$

Accepted Answer

A)  $x$-int: $(-8,0)$; $y$-int: $(0,1)$ 
B)  $x$-int: (9, 0); y-int: $(0,1)$ 
C)  $x$-int: $(-8,0)$; $y$ - int: none 
D)  $x$-int: none; $y$-int: $(0,1)$ 
A)  $x$-int: $(-8,0)$; $y$-int: $(0,1)$ 
B)  $x$-int: (9, 0); y-int: $(0,1)$ 
C)  $x$-int: $(-8,0)$; $y$ - int: none 
D)  $x$-int: none; $y$-int: $(0,1)$

Question 13

Solve.
-One method to determine the time since an animal died is to estimate the percentage of carbon- 14 remaining in its bones. The pencent $P$ in decimal form of carbon- 14 remaining $x$ years is given by $\mathrm{P}(\mathrm{x})=\mathrm{e}^{-0.000121 \mathrm{x}}$. Approximate (to the nearest whole year) the age of a fossil if there is $74 \%$ of carbon- 14 remaining.

Accepted Answer

A)  $-16,541$ 
B)  2488 
C)  $-35,571$ 
D)  1081 
A)  $-16,541$ 
B)  2488 
C)  $-35,571$ 
D)  1081

Question 14

Solve.
-$\log _{6}(6 x-9)=2$

Accepted Answer

A)  $\left\{\frac{\log _{6} 2+9}{6}\right\}$ 
B)  $\left\{\frac{45}{11}\right\}$ 
C)  $\{39\}$ 
D)  $\left\{\frac{15}{2}\right\}$ 
A)  $\left\{\frac{\log _{6} 2+9}{6}\right\}$ 
B)  $\left\{\frac{45}{11}\right\}$ 
C)  $\{39\}$ 
D)  $\left\{\frac{15}{2}\right\}$

Question 15

Determine whether function is one-to-one.
-The function that pairs the temperature in degrees Fahrenheit of a cup of coffee with its temperature in degrees Celsius.

Accepted Answer

A) True 
 B)False

Question 16

Given $g(x)$ and $(g \circ f)(x)$, find $f(x)$.
-$g(x)=2 x^{2}-7,(g \circ f)(x)=2 x^{2}-20 x+43$

Accepted Answer

A)  $f(x)=x-5$ 
B)  $f(x)=x+7$ 
C)  $f(x)=x+3$ 
D)  $f(x)=x-4$ 
A)  $f(x)=x-5$ 
B)  $f(x)=x+7$ 
C)  $f(x)=x+3$ 
D)  $f(x)=x-4$

Question 17

Solve the problem.
-Yearly sales of an electronic device S(t), in millions of dollars, tyears after 2009 can be estimated by
$$S(t)=300 \cdot 2^{t}$$
Determine the year in which sales reached $\$ 1500$ million.

Accepted Answer

A)  About 2011 
B)  About 2010 
C)  About 2009 
D)  About 2012 
A)  About 2011 
B)  About 2010 
C)  About 2009 
D)  About 2012

Question 18

Graph the piecewise function
-$$ f(x)= \begin{cases}2^{x}+1 & \text { if } x>0 \ -\frac{1}{4} x+2 & \text { if } x \leq 0\end{cases}$$

Accepted Answer

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

Question 19

Compute the compound interest.
-John Lee's savings account has a balance of $\$ 500$. After 5 years, what will the amount of interest be at $5 \%$ compounded annually? Round to the nearest dollar.

Accepted Answer

A)  $\$ 129$ 
B)  $\$ 25$ 
C)  $\$ 143$ 
D)  $\$ 138$ 
A)  $\$ 129$ 
B)  $\$ 25$ 
C)  $\$ 143$ 
D)  $\$ 138$

Question 20

Solve. Round to the nearest thousandth.
-$\mathrm{e}^{\mathrm{x}}-40 \mathrm{e}^{-\mathrm{x}}=3$

Accepted Answer

A)  $\{1.562,1.609\}$ 
B)  $\{1.609,2.079\}$ 
C)  $\{2.079\}$ 
D)  $\{1.609\}$ 
A)  $\{1.562,1.609\}$ 
B)  $\{1.609,2.079\}$ 
C)  $\{2.079\}$ 
D)  $\{1.609\}$

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

Given $f(x)$ and $g(x)$ , find the indicated composition and state its domain. - $f(x)=6 x+5, g(x)=4 x-1$ Find $(\mathrm{f} \circ \mathrm{g})(\mathrm{x})$ .

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

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

Solve the problem. -A certain country's population $\mathrm{P}(\mathrm{t})$ , in millions, tyears after 2010 can be approximated by $\mathrm{P}(\mathrm{t})=3.495(1.018)^{\mathrm{t}}$ . Find the doubling time. Round your answer to the nearest tenth.

The population growth of an animal species is described by $F(t)=700+90 \log 3(2 t+1)$ where $t$ is the number of months since the species was introduced. Find the population of this species in an area 4 month(s) after the species is introduced.

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

For the given functions $f(x)$ and $g(x)$ , find $(f \cdot g)(x)$ or $\left(\frac{f}{g}\right)(x)$ as indicated. - $f(x)=-9 x+4, g(x)=5 x^{2}-x+4$ Find $(\mathrm{f} \cdot \mathrm{g})(\mathrm{x})$ .

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

Given $f(x)$ and $g(x)$ , find the indicated composition and evaluate. - $f(x)=6 x+2 ; g(x)=x+7$ Find $(f \circ g)(4)$ .

Evaluate. Round to the nearest thousandth, if necessary. - $\log 100,000$

Find all intercepts for the given function. Round to the nearest tenth if necessary. - $f(x)=\log (x+9)$

Solve. - $\log _{6}(6 x-9)=2$

Determine whether function is one-to-one. -The function that pairs the temperature in degrees Fahrenheit of a cup of coffee with its temperature in degrees Celsius.

Given $g(x)$ and $(g \circ f)(x)$ , find $f(x)$ . - $g(x)=2 x^{2}-7,(g \circ f)(x)=2 x^{2}-20 x+43$

Solve the problem. -Yearly sales of an electronic device S(t), in millions of dollars, tyears after 2009 can be estimated by $S(t)=300 \cdot 2^{t}$ Determine the year in which sales reached $\$ 1500$ million.

Graph the piecewise function - $f(x)= \begin{cases}2^{x}+1 & \text { if } x>0 \\ -\frac{1}{4} x+2 & \text { if } x \leq 0\end{cases}$

Compute the compound interest. -John Lee's savings account has a balance of $\$ 500$ . After 5 years, what will the amount of interest be at $5 \%$ compounded annually? Round to the nearest dollar.

Solve. Round to the nearest thousandth. - $\mathrm{e}^{\mathrm{x}}-40 \mathrm{e}^{-\mathrm{x}}=3$

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 graph is the graph of a function. -

Given f(x)f(x)f(x) and g(x)g(x)g(x) , find the indicated composition and state its domain. - f(x)=6x+5,g(x)=4x−1f(x)=6 x+5, g(x)=4 x-1f(x)=6x+5,g(x)=4x−1 Find (f∘g)(x)(\mathrm{f} \circ \mathrm{g})(\mathrm{x})(f∘g)(x) .

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

For the given function f(x)f(x)f(x) , find f−1(x)f^{-1}(x)f−1(x) . State the domain of f−1(x)f^{-1}(x)f−1(x) . - f(x)=x+2f(x)=\sqrt{x+2}f(x)=x+2​

Solve the problem. -A certain country's population P(t)\mathrm{P}(\mathrm{t})P(t) , in millions, tyears after 2010 can be approximated by P(t)=3.495(1.018)t\mathrm{P}(\mathrm{t})=3.495(1.018)^{\mathrm{t}}P(t)=3.495(1.018)t . Find the doubling time. Round your answer to the nearest tenth.

The population growth of an animal species is described by F(t)=700+90log⁡3(2t+1)F(t)=700+90 \log 3(2 t+1)F(t)=700+90log3(2t+1) where ttt is the number of months since the species was introduced. Find the population of this species in an area 4 month(s) after the species is introduced.

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

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

Given f(x)f(x)f(x) and g(x)g(x)g(x) , find the indicated composition and evaluate. - f(x)=6x+2;g(x)=x+7f(x)=6 x+2 ; g(x)=x+7f(x)=6x+2;g(x)=x+7 Find (f∘g)(4)(f \circ g)(4)(f∘g)(4) .

Evaluate. Round to the nearest thousandth, if necessary. - log⁡100,000\log 100,000log100,000

Find all intercepts for the given function. Round to the nearest tenth if necessary. - f(x)=log⁡(x+9)f(x)=\log (x+9)f(x)=log(x+9)

Solve. - log⁡6(6x−9)=2\log _{6}(6 x-9)=2log6​(6x−9)=2

Determine whether function is one-to-one. -The function that pairs the temperature in degrees Fahrenheit of a cup of coffee with its temperature in degrees Celsius.

Given g(x)g(x)g(x) and (g∘f)(x)(g \circ f)(x)(g∘f)(x) , find f(x)f(x)f(x) . - g(x)=2x2−7,(g∘f)(x)=2x2−20x+43g(x)=2 x^{2}-7,(g \circ f)(x)=2 x^{2}-20 x+43g(x)=2x2−7,(g∘f)(x)=2x2−20x+43

Solve the problem. -Yearly sales of an electronic device S(t), in millions of dollars, tyears after 2009 can be estimated by S(t)=300⋅2tS(t)=300 \cdot 2^{t}S(t)=300⋅2t Determine the year in which sales reached $1500\$ 1500$1500 million.

Graph the piecewise function - f(x)={2x+1 if x>0−14x+2 if x≤0 f(x)= \begin{cases}2^{x}+1 & \text { if } x>0 \\ -\frac{1}{4} x+2 & \text { if } x \leq 0\end{cases}f(x)={2x+1−41​x+2​ if x>0 if x≤0​

Compute the compound interest. -John Lee's savings account has a balance of $500\$ 500$500 . After 5 years, what will the amount of interest be at 5%5 \%5% compounded annually? Round to the nearest dollar.

Solve. Round to the nearest thousandth. - ex−40e−x=3\mathrm{e}^{\mathrm{x}}-40 \mathrm{e}^{-\mathrm{x}}=3ex−40e−x=3

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

Given $f(x)$ and $g(x)$ , find the indicated composition and state its domain. - $f(x)=6 x+5, g(x)=4 x-1$ Find $(\mathrm{f} \circ \mathrm{g})(\mathrm{x})$ .

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

Solve the problem. -A certain country's population $\mathrm{P}(\mathrm{t})$ , in millions, tyears after 2010 can be approximated by $\mathrm{P}(\mathrm{t})=3.495(1.018)^{\mathrm{t}}$ . Find the doubling time. Round your answer to the nearest tenth.

The population growth of an animal species is described by $F(t)=700+90 \log 3(2 t+1)$ where $t$ is the number of months since the species was introduced. Find the population of this species in an area 4 month(s) after the species is introduced.

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

Given $f(x)$ and $g(x)$ , find the indicated composition and evaluate. - $f(x)=6 x+2 ; g(x)=x+7$ Find $(f \circ g)(4)$ .

Evaluate. Round to the nearest thousandth, if necessary. - $\log 100,000$

Find all intercepts for the given function. Round to the nearest tenth if necessary. - $f(x)=\log (x+9)$

Solve. - $\log _{6}(6 x-9)=2$

Given $g(x)$ and $(g \circ f)(x)$ , find $f(x)$ . - $g(x)=2 x^{2}-7,(g \circ f)(x)=2 x^{2}-20 x+43$

Solve the problem. -Yearly sales of an electronic device S(t), in millions of dollars, tyears after 2009 can be estimated by $S(t)=300 \cdot 2^{t}$ Determine the year in which sales reached $\$ 1500$ million.

Graph the piecewise function - $f(x)= \begin{cases}2^{x}+1 & \text { if } x>0 \\ -\frac{1}{4} x+2 & \text { if } x \leq 0\end{cases}$

Compute the compound interest. -John Lee's savings account has a balance of $\$ 500$ . After 5 years, what will the amount of interest be at $5 \%$ compounded annually? Round to the nearest dollar.

Solve. Round to the nearest thousandth. - $\mathrm{e}^{\mathrm{x}}-40 \mathrm{e}^{-\mathrm{x}}=3$