Question 1

Write the function F(x) as a composition of f, g, or h.
-$\begin{array} { l } 
\mathrm { f } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } - 8 \quad \mathrm {~g} ( \mathrm { x } ) = - 3 \mathrm { x } \quad \mathrm { h } ( \mathrm { x } ) = \sqrt { \mathrm { x } + 5 } \
\mathrm {~F} ( \mathrm { x } ) = \sqrt { \mathrm { x } ^ { 2 } - 3 }
\end{array}$

Accepted Answer

A)  $\mathrm { F } ( \mathrm { x } ) = ( h \circ f ) ( \mathrm { x } )$ 
B)  $F ( x ) = ( h \circ g ) ( x )$ 
C)  $F ( x ) = ( f \circ h ) ( x )$ 
D)  $\mathrm { F } ( \mathrm { x } ) = ( \mathrm { g } \circ \mathrm { h } ) ( \mathrm { x } )$ 
A)  $\mathrm { F } ( \mathrm { x } ) = ( h \circ f ) ( \mathrm { x } )$ 
B)  $F ( x ) = ( h \circ g ) ( x )$ 
C)  $F ( x ) = ( f \circ h ) ( x )$ 
D)  $\mathrm { F } ( \mathrm { x } ) = ( \mathrm { g } \circ \mathrm { h } ) ( \mathrm { x } )$

Question 2

Given the values of f and g, find the function value.
-$f ( 3 ) = 3 ; g ( - 13 ) = 3 \quad$ Find $( f \circ g ) ( - 13 )$.

Accepted Answer

A)  10 
B)  3 
C)  13 
D)  $- 3$ 
A)  10 
B)  3 
C)  13 
D)  $- 3$

Question 3

Write the expression as sums or differences of multiples of logarithms.
-$\log _ { 4 } \sqrt { 3 x }$

Accepted Answer

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

Question 4

Determine whether the function is a one-to-one function.
-$\mathrm { f } = \{ ( 6,3 ) , ( 7,3 ) , ( 8 , - 9 ) , ( 9,1 ) \}$

Accepted Answer

A)  one-to-one 
B)  not one-to-one 
A)  one-to-one 
B)  not one-to-one

Question 5

Express as the logarithm of a single expression. Assume that variables represent positive numbers.
-$\log _ { 10 } 3 + \log _ { 10 } \left( x ^ { 3 } - 4 \right) + \log _ { 10 } 2$

Accepted Answer

A)  $\log _ { 10 } \left( 3 x ^ { 3 } - 12 \right)$ 
B)  $\log _ { 10 } \left( x ^ { 3 } + 1 \right)$ 
C)  $\log _ { 10 } \left( 6 x ^ { 3 } - 24 \right)$ 
D)  $\log _ { 10 } \left( \mathrm { x } ^ { 3 } - 24 \right)$ 
A)  $\log _ { 10 } \left( 3 x ^ { 3 } - 12 \right)$ 
B)  $\log _ { 10 } \left( x ^ { 3 } + 1 \right)$ 
C)  $\log _ { 10 } \left( 6 x ^ { 3 } - 24 \right)$ 
D)  $\log _ { 10 } \left( \mathrm { x } ^ { 3 } - 24 \right)$

Question 6

Solve the equation.
-$\log _ { 2 } ( 7 x - 2 ) = \log _ { 2 } ( 5 x + 7 )$

Accepted Answer

A)  $\frac { 5 } { 2 }$ 
B)  $\varnothing$ 
C)  5 
D)  $\frac { 9 } { 2 }$ 
A)  $\frac { 5 } { 2 }$ 
B)  $\varnothing$ 
C)  5 
D)  $\frac { 9 } { 2 }$

Question 7

For the given functions f and g, find the composition.
-$f ( x ) = x ^ { 2 } + 4 x ; g ( x ) = x + 2 \quad$ Find $( g \circ f ) ( 2 )$

Accepted Answer

A)  14 
B)  32 
C)  48 
D)  16 
A)  14 
B)  32 
C)  48 
D)  16

Question 8

Solve the equation.
-$\log _ { 4 } x + \log _ { 4 } ( x - 15 ) = 2$

Accepted Answer

A)  16 
B)  $1 , - 16$ 
C)  $- 1,16$ 
D)  4 
A)  16 
B)  $1 , - 16$ 
C)  $- 1,16$ 
D)  4

Question 9

Fill in the blank with one of the words or phrases listed below. Some words or phrases may be used more than once. $$\begin{array} { l l l l } 
\text { inverse } & \text { common } & \text { composition symmetric } & \text { exponential } \
\text { vertical } & \text { logarithmic } & \text { natural } \quad \text { half-life } & \text { horizontal }
\end{array}$$
-The graphs of $f$ and $f ^ { - 1 }$ are_______ about the line $y = x$.

Accepted Answer

A)  inverse 
B)  vertical 
C)  symmetric 
D)  horizontal 
A)  inverse 
B)  vertical 
C)  symmetric 
D)  horizontal

Question 10

$\log _ { 10 } 600 - \log _ { 10 } 60 = 1$

Accepted Answer

A) True 
 B)False

Question 11

Solve the equation. Give an approximate solution to four decimal places.
-$e ^ { 4 x } = 7$

Accepted Answer

A)  $0.1980$ 
B)  $0.4865$ 
C)  $4.7570$ 
D)  $7.7836$ 
A)  $0.1980$ 
B)  $0.4865$ 
C)  $4.7570$ 
D)  $7.7836$

Question 12

Use the exponential decay formula with half-lives to find the final amount. Round to the nearest tenth when necessary.
-

Accepted Answer

A)  $547.1$ 
B)  $428.6$ 
C)  2 
D)  $22.1$ 
A)  $547.1$ 
B)  $428.6$ 
C)  2 
D)  $22.1$

Question 13

Determine whether the function is one-to-one. If it is one-to-one find an equation or a set of ordered pairs that defines
the inverse function of the given function.
-$f ( x ) = 3 - 2 x$

Accepted Answer

A)  one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { - \mathrm { x } + 3 } { 2 }$ 
B)  one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 3 - 2 \mathrm { x } }$ 
C)  one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } - 3 } { 2 }$ 
D)  not one-to-one 
A)  one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { - \mathrm { x } + 3 } { 2 }$ 
B)  one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 3 - 2 \mathrm { x } }$ 
C)  one-to-one; $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } - 3 } { 2 }$ 
D)  not one-to-one

Question 14

Solve the logarithmic equation for x. Give an exact solution
-$\log _ { 5 } x = - 3$

Accepted Answer

A)  2 
B)  $- 15$ 
C)  $\frac { 1 } { 243 }$ 
D)  $\frac { 1 } { 125 }$ 
A)  2 
B)  $- 15$ 
C)  $\frac { 1 } { 243 }$ 
D)  $\frac { 1 } { 125 }$

Question 15

Solve. Round the answer to the nearest whole number.
-If the annual population growth rate is $5.9 \%$, find how long will it take a population of birds to increase from 200 birds to 1100 birds.

Accepted Answer

A)  $119 y \mathrm { y }$ 
B)  $10 \mathrm { yr }$ 
C)  $29 \mathrm { yr }$ 
D)  $107 \mathrm { yr }$ 
A)  $119 y \mathrm { y }$ 
B)  $10 \mathrm { yr }$ 
C)  $29 \mathrm { yr }$ 
D)  $107 \mathrm { yr }$

Question 16

Solve the equation for x. Give an exact solution.
-$\ln \mathrm { x } = 3.8$

Accepted Answer

A)  $3.810$ 
B)  $e ^ { 3.8 }$ 
C)  $3.8 ^ { \mathrm { e } }$ 
D)  $10 ^ { 3.8 }$ 
A)  $3.810$ 
B)  $e ^ { 3.8 }$ 
C)  $3.8 ^ { \mathrm { e } }$ 
D)  $10 ^ { 3.8 }$

Question 17

Express as the logarithm of a single expression. Assume that variables represent positive numbers.
-$3 \log _ { 5 } x + \frac { 1 } { 6 } \log _ { 5 } x - 2 \log _ { 5 } ( x + 1 )$

Accepted Answer

A)  $\log _ { 5 } \frac { x ^ { 19 / 6 } } { ( x + 1 ) ^ { 2 } }$ 
B)  $\frac { 19 } { 6 } \log _ { 5 } \frac { x } { ( x + 1 ) ^ { 2 } }$ 
C)  $\log _ { 5 } \left( \frac { \frac { 19 } { 6 } x } { 2 ( x + 1 ) } \right)$ 
D)  $\log _ { 5 } \frac { x ^ { 19 / 6 } } { 2 ( x + 1 ) }$ 
A)  $\log _ { 5 } \frac { x ^ { 19 / 6 } } { ( x + 1 ) ^ { 2 } }$ 
B)  $\frac { 19 } { 6 } \log _ { 5 } \frac { x } { ( x + 1 ) ^ { 2 } }$ 
C)  $\log _ { 5 } \left( \frac { \frac { 19 } { 6 } x } { 2 ( x + 1 ) } \right)$ 
D)  $\log _ { 5 } \frac { x ^ { 19 / 6 } } { 2 ( x + 1 ) }$

Question 18

Write the expression as sums or differences of multiples of logarithms.
-$\log _ { 5 } \frac { 7 \cdot 11 } { 13 }$

Accepted Answer

A)  $\log _ { 5 } 5$ 
B)  $\log _ { 5 } \frac { 77 } { 13 }$ 
C)  $\log _ { 5 } 7 + \log _ { 5 } 11 - \log _ { 5 } 13$ 
D)  $\log _ { 5 } 77 - \log _ { 5 } 13$ 
A)  $\log _ { 5 } 5$ 
B)  $\log _ { 5 } \frac { 77 } { 13 }$ 
C)  $\log _ { 5 } 7 + \log _ { 5 } 11 - \log _ { 5 } 13$ 
D)  $\log _ { 5 } 77 - \log _ { 5 } 13$

Question 19

Solve. Round the answer to the nearest whole number.
-An accidental spill of 75 grams of radioactive material in a local stream has led to the presence of radioactive debris decaying at a rate of $3 \%$ each day. Find how much debris still remains after 8 days.

Accepted Answer

A)  $54 \mathrm {~g}$ 
B)  $4 \mathrm {~g}$ 
C)  $64 \mathrm {~g}$ 
D)  $59 \mathrm {~g}$ 
A)  $54 \mathrm {~g}$ 
B)  $4 \mathrm {~g}$ 
C)  $64 \mathrm {~g}$ 
D)  $59 \mathrm {~g}$

Question 20

Find the value of the logarithmic expression.
-$\log _ { 4 } \frac { 1 } { 16 }$

Accepted Answer

A)  2 
B)  $- 2$ 
C)  $- \frac { 1 } { 4 }$ 
D)  $\frac { 1 } { 2 }$ 
A)  2 
B)  $- 2$ 
C)  $- \frac { 1 } { 4 }$ 
D)  $\frac { 1 } { 2 }$

Write the function F(x) as a composition of f, g, or h. - ()=-8()=-3()= ()=

Given the values of f and g, find the function value. - $f ( 3 ) = 3 ; g ( - 13 ) = 3 \quad$ Find $( f \circ g ) ( - 13 )$ .

Write the expression as sums or differences of multiples of logarithms. - $\log _ { 4 } \sqrt { 3 x }$

Determine whether the function is a one-to-one function. - $\mathrm { f } = \{ ( 6,3 ) , ( 7,3 ) , ( 8 , - 9 ) , ( 9,1 ) \}$

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $\log _ { 10 } 3 + \log _ { 10 } \left( x ^ { 3 } - 4 \right) + \log _ { 10 } 2$

Solve the equation. - $\log _ { 2 } ( 7 x - 2 ) = \log _ { 2 } ( 5 x + 7 )$

For the given functions f and g, find the composition. - $f ( x ) = x ^ { 2 } + 4 x ; g ( x ) = x + 2 \quad$ Find $( g \circ f ) ( 2 )$

Solve the equation. - $\log _ { 4 } x + \log _ { 4 } ( x - 15 ) = 2$

Fill in the blank with one of the words or phrases listed below. Some words or phrases may be used more than once. inverse common composition symmetric exponential vertical logarithmic natural half-life horizontal -The graphs of $f$ and $f ^ { - 1 }$ are_______ about the line $y = x$ .

$\log _ { 10 } 600 - \log _ { 10 } 60 = 1$

Solve the equation. Give an approximate solution to four decimal places. - $e ^ { 4 x } = 7$

Use the exponential decay formula with half-lives to find the final amount. Round to the nearest tenth when necessary. -

Determine whether the function is one-to-one. If it is one-to-one find an equation or a set of ordered pairs that defines the inverse function of the given function. - $f ( x ) = 3 - 2 x$

Solve the logarithmic equation for x. Give an exact solution - $\log _ { 5 } x = - 3$

Solve. Round the answer to the nearest whole number. -If the annual population growth rate is $5.9 \%$ , find how long will it take a population of birds to increase from 200 birds to 1100 birds.

Solve the equation for x. Give an exact solution. - $\ln \mathrm { x } = 3.8$

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $3 \log _ { 5 } x + \frac { 1 } { 6 } \log _ { 5 } x - 2 \log _ { 5 } ( x + 1 )$

Write the expression as sums or differences of multiples of logarithms. - $\log _ { 5 } \frac { 7 \cdot 11 } { 13 }$

Solve. Round the answer to the nearest whole number. -An accidental spill of 75 grams of radioactive material in a local stream has led to the presence of radioactive debris decaying at a rate of $3 \%$ each day. Find how much debris still remains after 8 days.

Find the value of the logarithmic expression. - $\log _ { 4 } \frac { 1 } { 16 }$

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 12: Exponential and Logarithmic Functions

Write the function F(x) as a composition of f, g, or h. - ()=-8()=-3()= ()=

Given the values of f and g, find the function value. - f(3)=3;g(−13)=3f ( 3 ) = 3 ; g ( - 13 ) = 3 \quadf(3)=3;g(−13)=3 Find (f∘g)(−13)( f \circ g ) ( - 13 )(f∘g)(−13) .

Write the expression as sums or differences of multiples of logarithms. - log⁡43x\log _ { 4 } \sqrt { 3 x }log4​3x​

Determine whether the function is a one-to-one function. - f={(6,3),(7,3),(8,−9),(9,1)}\mathrm { f } = \{ ( 6,3 ) , ( 7,3 ) , ( 8 , - 9 ) , ( 9,1 ) \}f={(6,3),(7,3),(8,−9),(9,1)}

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - log⁡103+log⁡10(x3−4)+log⁡102\log _ { 10 } 3 + \log _ { 10 } \left( x ^ { 3 } - 4 \right) + \log _ { 10 } 2log10​3+log10​(x3−4)+log10​2

Solve the equation. - log⁡2(7x−2)=log⁡2(5x+7)\log _ { 2 } ( 7 x - 2 ) = \log _ { 2 } ( 5 x + 7 )log2​(7x−2)=log2​(5x+7)

For the given functions f and g, find the composition. - f(x)=x2+4x;g(x)=x+2f ( x ) = x ^ { 2 } + 4 x ; g ( x ) = x + 2 \quadf(x)=x2+4x;g(x)=x+2 Find (g∘f)(2)( g \circ f ) ( 2 )(g∘f)(2)

Solve the equation. - log⁡4x+log⁡4(x−15)=2\log _ { 4 } x + \log _ { 4 } ( x - 15 ) = 2log4​x+log4​(x−15)=2

Fill in the blank with one of the words or phrases listed below. Some words or phrases may be used more than once. inverse common composition symmetric exponential vertical logarithmic natural half-life horizontal -The graphs of fff and f−1f ^ { - 1 }f−1 are_______ about the line y=xy = xy=x .

log⁡10600−log⁡1060=1\log _ { 10 } 600 - \log _ { 10 } 60 = 1log10​600−log10​60=1

Solve the equation. Give an approximate solution to four decimal places. - e4x=7e ^ { 4 x } = 7e4x=7

Use the exponential decay formula with half-lives to find the final amount. Round to the nearest tenth when necessary. -

Determine whether the function is one-to-one. If it is one-to-one find an equation or a set of ordered pairs that defines the inverse function of the given function. - f(x)=3−2xf ( x ) = 3 - 2 xf(x)=3−2x

Solve the logarithmic equation for x. Give an exact solution - log⁡5x=−3\log _ { 5 } x = - 3log5​x=−3

Solve. Round the answer to the nearest whole number. -If the annual population growth rate is 5.9%5.9 \%5.9% , find how long will it take a population of birds to increase from 200 birds to 1100 birds.

Solve the equation for x. Give an exact solution. - ln⁡x=3.8\ln \mathrm { x } = 3.8lnx=3.8

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - 3log⁡5x+16log⁡5x−2log⁡5(x+1)3 \log _ { 5 } x + \frac { 1 } { 6 } \log _ { 5 } x - 2 \log _ { 5 } ( x + 1 )3log5​x+61​log5​x−2log5​(x+1)

Write the expression as sums or differences of multiples of logarithms. - log⁡57⋅1113\log _ { 5 } \frac { 7 \cdot 11 } { 13 }log5​137⋅11​

Solve. Round the answer to the nearest whole number. -An accidental spill of 75 grams of radioactive material in a local stream has led to the presence of radioactive debris decaying at a rate of 3%3 \%3% each day. Find how much debris still remains after 8 days.

Find the value of the logarithmic expression. - log⁡4116\log _ { 4 } \frac { 1 } { 16 }log4​161​

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Given the values of f and g, find the function value. - $f ( 3 ) = 3 ; g ( - 13 ) = 3 \quad$ Find $( f \circ g ) ( - 13 )$ .

Write the expression as sums or differences of multiples of logarithms. - $\log _ { 4 } \sqrt { 3 x }$

Determine whether the function is a one-to-one function. - $\mathrm { f } = \{ ( 6,3 ) , ( 7,3 ) , ( 8 , - 9 ) , ( 9,1 ) \}$

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $\log _ { 10 } 3 + \log _ { 10 } \left( x ^ { 3 } - 4 \right) + \log _ { 10 } 2$

Solve the equation. - $\log _ { 2 } ( 7 x - 2 ) = \log _ { 2 } ( 5 x + 7 )$

For the given functions f and g, find the composition. - $f ( x ) = x ^ { 2 } + 4 x ; g ( x ) = x + 2 \quad$ Find $( g \circ f ) ( 2 )$

Solve the equation. - $\log _ { 4 } x + \log _ { 4 } ( x - 15 ) = 2$

Fill in the blank with one of the words or phrases listed below. Some words or phrases may be used more than once. inverse common composition symmetric exponential vertical logarithmic natural half-life horizontal -The graphs of $f$ and $f ^ { - 1 }$ are_______ about the line $y = x$ .

$\log _ { 10 } 600 - \log _ { 10 } 60 = 1$

Solve the equation. Give an approximate solution to four decimal places. - $e ^ { 4 x } = 7$

Determine whether the function is one-to-one. If it is one-to-one find an equation or a set of ordered pairs that defines the inverse function of the given function. - $f ( x ) = 3 - 2 x$

Solve the logarithmic equation for x. Give an exact solution - $\log _ { 5 } x = - 3$

Solve. Round the answer to the nearest whole number. -If the annual population growth rate is $5.9 \%$ , find how long will it take a population of birds to increase from 200 birds to 1100 birds.

Solve the equation for x. Give an exact solution. - $\ln \mathrm { x } = 3.8$

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $3 \log _ { 5 } x + \frac { 1 } { 6 } \log _ { 5 } x - 2 \log _ { 5 } ( x + 1 )$

Write the expression as sums or differences of multiples of logarithms. - $\log _ { 5 } \frac { 7 \cdot 11 } { 13 }$

Solve. Round the answer to the nearest whole number. -An accidental spill of 75 grams of radioactive material in a local stream has led to the presence of radioactive debris decaying at a rate of $3 \%$ each day. Find how much debris still remains after 8 days.

Find the value of the logarithmic expression. - $\log _ { 4 } \frac { 1 } { 16 }$