Question 1

Provide an appropriate response.
-If $f ( x ) = x , g ( x ) = x - 11$, and $h ( x ) = x ^ { 2 } - 7 x + 5$, find the composition $( f \circ h ) ( 0 )$.

Accepted Answer

A)  $- 11$ 
B)  5 
C)  0 
D)  $- 2$ 
A)  $- 11$ 
B)  5 
C)  0 
D)  $- 2$

Question 2

Determine whether the functions f and g are inverses of each other.
-$$f ( x ) = 4 x + 5 ; g ( x ) = \frac { x - 5 } { 4 }$$

Accepted Answer

A)  Yes 
B)  $\mathrm { No }$ 
A)  Yes 
B)  $\mathrm { No }$

Question 3

Find the value of the logarithmic expression.
-$\log _ { 10 } 1000$

Accepted Answer

A)  $- 3$ 
B)  $\frac { 1 } { 1000 }$ 
C)  30 
D)  3 
A)  $- 3$ 
B)  $\frac { 1 } { 1000 }$ 
C)  30 
D)  3

Question 4

If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs.
-$\begin{array}{l|c|c|c|c|c|c}
\text { Month of } 1999 \text { (input) } & \text { Jan } & \text { Feb } & \text { Mar } & \text { Apr } & \text { May } & \text { Jun } \
\hline \begin{array}{l}
\text { Sales of Product A } \
\text { (output) }
\end{array} & 5010 & 5139 & 5526 & 6042 & 5397 & 5655
\end{array}$

Accepted Answer

A) $\begin{array}{l|l|l|l|l|l|l}
\text { Month of } 1999 \text { (input) } & \text { Jan } & \text { Feb } & \text { Mar } & \text { Apr } & \text { May } & \text { Jun } \
\hline \text { Sales of Product A } & & & & & & \
\text { (output) } & 5010 & 5139 & 5526 & 6042 & 5397 & 5655
\end{array}$ 
B) $\begin{array}{l|c|c|c|c|c|c}
\text { Sales of Product A } & & & & & & \
\text { (input) } & 5010 & 5139 & 5526 & 6042 & 5397 & 5655 \
\hline \text { Month of } 1999 \text { (output) } & \text { Jan } & \text { Feb } & \text { Mar } & \text { Apr } & \text { May } & \text { Jun }
\end{array}$ 
C) $\begin{array}{l|c|c|c|c|c|c}
\text { Sales of Product A } & & & & & & \
\text { (input) } & 5010 & 5139 & 5526 & 5397 & 6042 & 5655 \
\hline \text { Month of } 1999 \text { (output) } & \text { Jan } & \text { Feb } & \text { Mar } & \text { Apr } & \text { May } & \text { Jun }
\end{array}$ 
D) $\text { not one-to-one }$ 
A) $\begin{array}{l|l|l|l|l|l|l}
\text { Month of } 1999 \text { (input) } & \text { Jan } & \text { Feb } & \text { Mar } & \text { Apr } & \text { May } & \text { Jun } \
\hline \text { Sales of Product A } & & & & & & \
\text { (output) } & 5010 & 5139 & 5526 & 6042 & 5397 & 5655
\end{array}$ 
B) $\begin{array}{l|c|c|c|c|c|c}
\text { Sales of Product A } & & & & & & \
\text { (input) } & 5010 & 5139 & 5526 & 6042 & 5397 & 5655 \
\hline \text { Month of } 1999 \text { (output) } & \text { Jan } & \text { Feb } & \text { Mar } & \text { Apr } & \text { May } & \text { Jun }
\end{array}$ 
C) $\begin{array}{l|c|c|c|c|c|c}
\text { Sales of Product A } & & & & & & \
\text { (input) } & 5010 & 5139 & 5526 & 5397 & 6042 & 5655 \
\hline \text { Month of } 1999 \text { (output) } & \text { Jan } & \text { Feb } & \text { Mar } & \text { Apr } & \text { May } & \text { Jun }
\end{array}$ 
D) $\text { not one-to-one }$

Question 5

Fill in the blank with one of the words or phrases listed below. Some words or phrases may be used more than once. $$\begin{array} { l l l l } 
\text { inverse } & \text { common } & \text { composition symmetric } & \text { exponential } \
\text { vertical } & \text { logarithmic } & \text { natural half-life } & \text { horizontal }
\end{array}$$
-is the amount of time it takes for half of the amount of a substance to decay.

Accepted Answer

A)  Exponential 
B)  Logarithmic 
C)  Half-life 
D)  Composition 
A)  Exponential 
B)  Logarithmic 
C)  Half-life 
D)  Composition

Question 6

Find the value of the logarithmic expression.
-$\log _ { 10 } \frac { 1 } { 100 }$

Accepted Answer

A)  2 
B)  $- 20$ 
C)  100 
D)  $- 2$ 
A)  2 
B)  $- 20$ 
C)  100 
D)  $- 2$

Question 7

Solve. Round the answer to the nearest whole.
-Suppose a city with population 320,000 has been growing at a rate of 4% per year. If this rate continues, find the population of this city in 15 years.

Accepted Answer

A)  665,257 
B)  559,682 
C)  576,302 
D)  498,550 
A)  665,257 
B)  559,682 
C)  576,302 
D)  498,550

Question 8

Solve.
-Find out how long it takes a $\$ 3100$ investment to double if it is invested at $8 \%$ compounded semiannually. Round to the nearest tenth of a year. Use the formula $A = P \left( 1 + \frac { r } { n } \right) ^ { n t }$.

Accepted Answer

A)  $8.6$ years 
B)  9 years 
C)  $9.2$ years 
D)  $8.8$ years 
A)  $8.6$ years 
B)  9 years 
C)  $9.2$ years 
D)  $8.8$ years

Question 9

Solve for x.
-$$\log _ { 216 } x = \frac { 1 } { 3 }$$

Accepted Answer

A)  $\{ - 6 \}$ 
B)  $\{ 6 \}$ 
C)  $\{ 2 \}$ 
D)  $\{ 36 \}$ 
A)  $\{ - 6 \}$ 
B)  $\{ 6 \}$ 
C)  $\{ 2 \}$ 
D)  $\{ 36 \}$

Question 10

Find the inverse of the one-to-one function.
-$$f ( x ) = ( x + 7 ) ^ { 3 } - 3$$

Accepted Answer

A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } + 3 } - 7$ 
B)  $f ^ { - 1 } ( x ) = - \sqrt [ 3 ] { x + 3 } + 7$ 
C)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x + 3 } + 7$ 
D)  $f ( x ) = ( x + 3 ) ^ { 3 } - 7$ 
A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } + 3 } - 7$ 
B)  $f ^ { - 1 } ( x ) = - \sqrt [ 3 ] { x + 3 } + 7$ 
C)  $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x + 3 } + 7$ 
D)  $f ( x ) = ( x + 3 ) ^ { 3 } - 7$

Question 11

Solve.
-The size of the coyote population at a national park increases at the rate of $4.9 \%$ per year. If the size of the current population is 123 , find how many coyotes there should be in 7 years. Use $\mathrm { y } = \mathrm { y } _ { 0 } \mathrm { e } ^ { 0.049 t }$ and round to the nearest whole number.

Accepted Answer

A)  175 
B)  171 
C)  173 
D)  177 
A)  175 
B)  171 
C)  173 
D)  177

Question 12

For the given functions f and g, find the composition.
-$$f ( x ) = 6 x ^ { 2 } - 2 x ; g ( x ) = - 3 x$$
Find $( g \circ f ) ( x )$.

Accepted Answer

A)  $54 x ^ { 2 } - 2 x$ 
B)  $6 x ^ { 2 } - 4$ 
C)  $- 18 x ^ { 3 } + 6 x ^ { 2 }$ 
D)  $- 18 x ^ { 2 } + 6 x$ 
A)  $54 x ^ { 2 } - 2 x$ 
B)  $6 x ^ { 2 } - 4$ 
C)  $- 18 x ^ { 3 } + 6 x ^ { 2 }$ 
D)  $- 18 x ^ { 2 } + 6 x$

Question 13

$f ( x ) = 3 x ^ { 8 } ; g ( x ) = 8 x ^ { 7 }$
Find $( f \cdot g ) ( x )$

Accepted Answer

A)  $( f \cdot g ) ( x ) = 24 x ^ { 56 }$ 
B)  $( f \cdot g ) ( x ) = 24 x ^{15}$ 
C)  $( f \cdot g ) ( x ) = - 24 x ^ { 15 }$ 
D)  $( f \cdot g ) ( x ) = - 24 x ^ { 56 }$ 
A)  $( f \cdot g ) ( x ) = 24 x ^ { 56 }$ 
B)  $( f \cdot g ) ( x ) = 24 x ^{15}$ 
C)  $( f \cdot g ) ( x ) = - 24 x ^ { 15 }$ 
D)  $( f \cdot g ) ( x ) = - 24 x ^ { 56 }$

Question 14

Use the formula A $$A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { or } A = P e ^ { r t } \text { to solve. }$$
-How long it will take $4000 to grow to $6000 if the money is invested 4% interest compounded semiannually. Round to the nearest whole year.

Accepted Answer

A)  11 years 
B)  1 year 
C)  20 years 
D)  10 years 
A)  11 years 
B)  1 year 
C)  20 years 
D)  10 years

Question 15

Find the exact value.
-$\log \left( \frac { 1 } { 100 } \right)$

Accepted Answer

A)  $- \frac { 1 } { 2 }$ 
B)  $- 2$ 
C)  2 
D)  $\frac { 1 } { 100 }$ 
A)  $- \frac { 1 } { 2 }$ 
B)  $- 2$ 
C)  2 
D)  $\frac { 1 } { 100 }$

Question 16

Graph the function.
-$f(x)=\left(\frac{1}{2}\right)^{x}+2$

Accepted Answer

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

Question 17

Write as a logarithmic equation.
-$$11 ^ { 1 / 2 } = \sqrt { 11 }$$

Accepted Answer

A)  $\log _ { 11 } \frac { 1 } { 2 } = \sqrt { 11 }$ 
B)  $\log _ { 11 } \sqrt { 11 } = \frac { 1 } { 2 }$ 
C)  $\log _ { 1 / 2 } \sqrt { 11 } = 11$ 
D)  $\log _ { 1 / 2 } 11 = \sqrt { 11 }$ 
A)  $\log _ { 11 } \frac { 1 } { 2 } = \sqrt { 11 }$ 
B)  $\log _ { 11 } \sqrt { 11 } = \frac { 1 } { 2 }$ 
C)  $\log _ { 1 / 2 } \sqrt { 11 } = 11$ 
D)  $\log _ { 1 / 2 } 11 = \sqrt { 11 }$

Question 18

Solve.
-The rabbit population in a forest area grows at the rate of 6% monthly. If there are 300 rabbits in April, find how many rabbits (rounded to the nearest whole number) should be expected by next April. $$\text { Use } y = 300 ( 2.7 ) ^ { 0.06 t }$$

Accepted Answer

A)  613 
B)  583 
C)  600 
D)  626 
A)  613 
B)  583 
C)  600 
D)  626

Question 19

Use a calculator to approximate the logarithm to four decimal places.
-$\log 2.93$

Accepted Answer

A)  $0.4518$ 
B)  $0.4669$ 
C)  $1.0750$ 
D)  $0.4814$ 
A)  $0.4518$ 
B)  $0.4669$ 
C)  $1.0750$ 
D)  $0.4814$

Question 20

For the given functions f and g, find the composition.
-$$f ( x ) = x ^ { 2 } + 6 x ; g ( x ) = x + 3$$
Find $( g \circ f ) ( 2 )$.

Accepted Answer

A)  19 
B)  21 
C)  80 
D)  55 
A)  19 
B)  21 
C)  80 
D)  55

Provide an appropriate response. -If $f ( x ) = x , g ( x ) = x - 11$ , and $h ( x ) = x ^ { 2 } - 7 x + 5$ , find the composition $( f \circ h ) ( 0 )$ .

Determine whether the functions f and g are inverses of each other. - $f ( x ) = 4 x + 5 ; g ( x ) = \frac { x - 5 } { 4 }$

Find the value of the logarithmic expression. - $\log _ { 10 } 1000$

If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs. - Month of 1999 (input) Jan Feb Mar Apr May Jun Sales of Product A (output) 5010 5139 5526 6042 5397 5655

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 -is the amount of time it takes for half of the amount of a substance to decay.

Find the value of the logarithmic expression. - $\log _ { 10 } \frac { 1 } { 100 }$

Solve. Round the answer to the nearest whole. -Suppose a city with population 320,000 has been growing at a rate of 4% per year. If this rate continues, find the population of this city in 15 years.

Solve. -Find out how long it takes a $\$ 3100$ investment to double if it is invested at $8 \%$ compounded semiannually. Round to the nearest tenth of a year. Use the formula $A = P \left( 1 + \frac { r } { n } \right) ^ { n t }$ .

Solve for x. - $\log _ { 216 } x = \frac { 1 } { 3 }$

Find the inverse of the one-to-one function. - $f ( x ) = ( x + 7 ) ^ { 3 } - 3$

For the given functions f and g, find the composition. - $f ( x ) = 6 x ^ { 2 } - 2 x ; g ( x ) = - 3 x$ Find $( g \circ f ) ( x )$ .

$f ( x ) = 3 x ^ { 8 } ; g ( x ) = 8 x ^ { 7 }$ Find $( f \cdot g ) ( x )$

Use the formula A $A = P \left( 1 + \frac { r } { n } \right) ^ { n t } \text { or } A = P e ^ { r t } \text { to solve. }$ -How long it will take $4000 to grow to $6000 if the money is invested 4% interest compounded semiannually. Round to the nearest whole year.

Find the exact value. - $\log \left( \frac { 1 } { 100 } \right)$

Graph the function. - $f(x)=\left(\frac{1}{2}\right)^{x}+2$ $Graph the function. - f(x)=\left(\frac{1}{2}\right)^{x}+2$

Write as a logarithmic equation. - $11 ^ { 1 / 2 } = \sqrt { 11 }$

Solve. -The rabbit population in a forest area grows at the rate of 6% monthly. If there are 300 rabbits in April, find how many rabbits (rounded to the nearest whole number) should be expected by next April. $\text { Use } y = 300 ( 2.7 ) ^ { 0.06 t }$

Use a calculator to approximate the logarithm to four decimal places. - $\log 2.93$

For the given functions f and g, find the composition. - $f ( x ) = x ^ { 2 } + 6 x ; g ( x ) = x + 3$ Find $( g \circ f ) ( 2 )$ .

Real Numbers and Algebraic Expressions

Equations, Inequalities, and Problem Solving

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Conic Sections

Fractions

Filters

Exam 9: Exponential and Logarithmic Functions

Provide an appropriate response. -If f(x)=x,g(x)=x−11f ( x ) = x , g ( x ) = x - 11f(x)=x,g(x)=x−11 , and h(x)=x2−7x+5h ( x ) = x ^ { 2 } - 7 x + 5h(x)=x2−7x+5 , find the composition (f∘h)(0)( f \circ h ) ( 0 )(f∘h)(0) .

Determine whether the functions f and g are inverses of each other. - f(x)=4x+5;g(x)=x−54f ( x ) = 4 x + 5 ; g ( x ) = \frac { x - 5 } { 4 }f(x)=4x+5;g(x)=4x−5​

Find the value of the logarithmic expression. - log⁡101000\log _ { 10 } 1000log10​1000