Question 1

Find the exact value.
-$\log 100$

Accepted Answer

A)  $\frac { 1 } { 2 }$ 
B)  $\frac { 1 } { 5 }$ 
C)  2 
D)  20 
A)  $\frac { 1 } { 2 }$ 
B)  $\frac { 1 } { 5 }$ 
C)  2 
D)  20

Question 2

Solve the equation. Give an approximate solution to four decimal places.
-$$\mathrm { e } ^ { 2 \mathrm { x } } = 7$$

Accepted Answer

A)  $\{ 3.8918 \}$ 
B)  $\{ 0.0990 \}$ 
C)  $\{ 0.9730 \}$ 
D)  $\{ 9.5140 \}$ 
A)  $\{ 3.8918 \}$ 
B)  $\{ 0.0990 \}$ 
C)  $\{ 0.9730 \}$ 
D)  $\{ 9.5140 \}$

Question 3

Provide an appropriate response.
-If $f ( x ) = x , g ( x ) = x - 1$, and $h ( x ) = x ^ { 2 } - 5 x + 5$, find the composition $( g \circ f ) ( x )$.

Accepted Answer

A)  $x ^ { 2 } - 5 x + 5$ 
B)  $x - 1$ 
C)  $x ^ { 2 } - 1 x$ 
D)  $- 1$ 
A)  $x ^ { 2 } - 5 x + 5$ 
B)  $x - 1$ 
C)  $x ^ { 2 } - 1 x$ 
D)  $- 1$

Question 4

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

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 5

Provide an appropriate response.
-If $f ( x ) = x$ and $g ( x ) = 7 x - 5$, find $( f - g ) ( x )$

Accepted Answer

A)  $5 x - 6 x ^ { 2 }$ 
B)  $2 \mathrm { x }$ 
C)  $5 - 6 x$ 
D)  $- 6 x - 5$ 
A)  $5 x - 6 x ^ { 2 }$ 
B)  $2 \mathrm { x }$ 
C)  $5 - 6 x$ 
D)  $- 6 x - 5$

Question 6

f(x)=4 x-1 ; g(x)=6 x-2 
Find $( f \cdot g ) ( x )$

Accepted Answer

A)  $( f \cdot g ) ( x ) = 24 x ^ { 2 } - 8 x + 2$ 
B)  $( f \cdot g ) ( x ) = 10 x ^ { 2 } - 14 x - 3$ 
C)  $( f \cdot g ) ( x ) = 24 x ^ { 2 } + 2$ 
D)  $( f \cdot g ) ( x ) = 24 x ^ { 2 } - 14 x + 2$ 
A)  $( f \cdot g ) ( x ) = 24 x ^ { 2 } - 8 x + 2$ 
B)  $( f \cdot g ) ( x ) = 10 x ^ { 2 } - 14 x - 3$ 
C)  $( f \cdot g ) ( x ) = 24 x ^ { 2 } + 2$ 
D)  $( f \cdot g ) ( x ) = 24 x ^ { 2 } - 14 x + 2$

Question 7

Solve the equation.
-$$2 ^ { ( 3 x - 7 ) } = 4$$

Accepted Answer

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

Question 8

Find the value of the logarithmic expression.
-$8 ^ { \log _ { 8 } 15 }$

Accepted Answer

A)  $\log _ { 8 } 15$ 
B)  23 
C)  15 
D)  8 
A)  $\log _ { 8 } 15$ 
B)  23 
C)  15 
D)  8

Question 9

Graph the inverse of the function on the same set of axes.
-

Accepted Answer

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

Question 10

Graph the exponential function.
-$f(x)=3^{x}$

Accepted Answer

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

Question 11

Solve the equation.
-$$\log _ { 3 } 7 - \log _ { 3 } x = 3$$

Accepted Answer

A)  $\left\{ \frac { 27 } { 7 } \right\}$ 
B)  $\left\{ \frac { 7 } { 9 } \right\}$ 
C)  $\left\{ \frac { 7 } { 27 } \right\}$ 
D)  $\left\{ \frac { 7 } { 3 } \right\}$ 
A)  $\left\{ \frac { 27 } { 7 } \right\}$ 
B)  $\left\{ \frac { 7 } { 9 } \right\}$ 
C)  $\left\{ \frac { 7 } { 27 } \right\}$ 
D)  $\left\{ \frac { 7 } { 3 } \right\}$

Question 12

Approximate the logarithm to four decimal places using the change of base formula.
-$\log _ { 2 } 5$

Accepted Answer

A)  $2.3219$ 
B)  $0.3979$ 
C)  $1.0000$ 
D)  $0.4307$ 
A)  $2.3219$ 
B)  $0.3979$ 
C)  $1.0000$ 
D)  $0.4307$

Question 13

Graph the inverse of the function on the same set of axes.
-

Accepted Answer

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

Question 14

Provide an appropriate response.
-Approximate $\log _ { 5 } 9$ to four decimal places.

Accepted Answer

A)  $0.5878$ 
B)  $1.3652$ 
C)  $6.2907$ 
D)  $0.7325$ 
A)  $0.5878$ 
B)  $1.3652$ 
C)  $6.2907$ 
D)  $0.7325$

Question 15

Solve for x.
-$\log _ { \mathrm { X } } 36 = 2$

Accepted Answer

A)  $\{ 18 \}$ 
B)  $\{ 0.01 \}$ 
C)  $\{ - 6,6 \}$ 
D)  $\{ 6 \}$ 
A)  $\{ 18 \}$ 
B)  $\{ 0.01 \}$ 
C)  $\{ - 6,6 \}$ 
D)  $\{ 6 \}$

Question 16

Solve.
-Find out how long it takes a $\$ 3000$ investment to earn $\$ 400$ interest if it is invested at $9 \%$ compounded semiannually. Round to the nearest tenth of a year. Use the formula $A = \mathrm { P } \left( 1 + \frac { \mathrm { r } } { \mathrm { n } } \right) ^ { n t }$.

Accepted Answer

A)  $1.6$ years 
B)  $1.8$ years 
C)  $1.2$ years 
D)  $1.4$ years 
A)  $1.6$ years 
B)  $1.8$ years 
C)  $1.2$ years 
D)  $1.4$ years

Question 17

Solve. Round the answer to the nearest whole.
-The size of the coyote population at a national park increases at the rate of 4.4% per year. If the size of the current population is 140, find how many coyotes there will be in 7 years.

Accepted Answer

A)  193 coyotes 
B)  191 coyotes 
C)  187 coyotes 
D)  189 coyotes 
A)  193 coyotes 
B)  191 coyotes 
C)  187 coyotes 
D)  189 coyotes

Question 18

Use the following approximations to find the approximate value of the logarithmic expression: $\log _ { b } 3 \approx 0.5$ logb $8 \approx 0.9$
$\log _ { b } 5 \approx 0.7$ logb $20 \approx 1.3$
-$\log _ { \mathrm { b } } 125$

Accepted Answer

A)  $0.343$ 
B)  $0.23$ 
C)  $2.1$ 
D)  $3.7$ 
A)  $0.343$ 
B)  $0.23$ 
C)  $2.1$ 
D)  $3.7$

Question 19

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

Accepted Answer

A)  $2 \sqrt { 5 }$ 
B)  $\sqrt { 7 }$ 
C)  $\sqrt { 10 }$ 
D)  $2 \sqrt { 10 }$ 
A)  $2 \sqrt { 5 }$ 
B)  $\sqrt { 7 }$ 
C)  $\sqrt { 10 }$ 
D)  $2 \sqrt { 10 }$

Question 20

Determine whether the function is a one-to-one function.
-$$f = \{ ( - 8 , - 6 ) , ( - 18 , - 6 ) , ( - 5,8 ) \}$$

Accepted Answer

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

Find the exact value. - $\log 100$

Solve the equation. Give an approximate solution to four decimal places. - $\mathrm { e } ^ { 2 \mathrm { x } } = 7$

Provide an appropriate response. -If $f ( x ) = x , g ( x ) = x - 1$ , and $h ( x ) = x ^ { 2 } - 5 x + 5$ , find the composition $( g \circ f ) ( x )$ .

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

Provide an appropriate response. -If $f ( x ) = x$ and $g ( x ) = 7 x - 5$ , find $( f - g ) ( x )$

f(x)=4 x-1 ; g(x)=6 x-2 Find $( f \cdot g ) ( x )$

Solve the equation. - $2 ^ { ( 3 x - 7 ) } = 4$

Find the value of the logarithmic expression. - $8 ^ { \log _ { 8 } 15 }$

Graph the inverse of the function on the same set of axes. -

Graph the exponential function. - $f(x)=3^{x}$ $Graph the exponential function. - f(x)=3^{x}$

Solve the equation. - $\log _ { 3 } 7 - \log _ { 3 } x = 3$

Approximate the logarithm to four decimal places using the change of base formula. - $\log _ { 2 } 5$

Graph the inverse of the function on the same set of axes. -

Provide an appropriate response. -Approximate $\log _ { 5 } 9$ to four decimal places.

Solve for x. - $\log _ { \mathrm { X } } 36 = 2$

Solve. -Find out how long it takes a $\$ 3000$ investment to earn $\$ 400$ interest if it is invested at $9 \%$ compounded semiannually. Round to the nearest tenth of a year. Use the formula $A = \mathrm { P } \left( 1 + \frac { \mathrm { r } } { \mathrm { n } } \right) ^ { n t }$ .

Solve. Round the answer to the nearest whole. -The size of the coyote population at a national park increases at the rate of 4.4% per year. If the size of the current population is 140, find how many coyotes there will be in 7 years.

Use the following approximations to find the approximate value of the logarithmic expression: $\log _ { b } 3 \approx 0.5$ logb $8 \approx 0.9$ $\log _ { b } 5 \approx 0.7$ logb $20 \approx 1.3$ - $\log _ { \mathrm { b } } 125$

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

Determine whether the function is a one-to-one function. - $f = \{ ( - 8 , - 6 ) , ( - 18 , - 6 ) , ( - 5,8 ) \}$

Real Numbers and Algebraic Expressions

Equations, Inequalities, and Problem Solving

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Systems of Equations and Inequalities

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Exam 9: Exponential and Logarithmic Functions

Find the exact value. - log⁡100\log 100log100

Solve the equation. Give an approximate solution to four decimal places. - e2x=7\mathrm { e } ^ { 2 \mathrm { x } } = 7e2x=7

Provide an appropriate response. -If f(x)=x,g(x)=x−1f ( x ) = x , g ( x ) = x - 1f(x)=x,g(x)=x−1 , and h(x)=x2−5x+5h ( x ) = x ^ { 2 } - 5 x + 5h(x)=x2−5x+5 , find the composition (g∘f)(x)( g \circ f ) ( x )(g∘f)(x) .

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

Provide an appropriate response. -If f(x)=xf ( x ) = xf(x)=x and g(x)=7x−5g ( x ) = 7 x - 5g(x)=7x−5 , find (f−g)(x)( f - g ) ( x )(f−g)(x)

f(x)=4 x-1 ; g(x)=6 x-2 Find (f⋅g)(x)( f \cdot g ) ( x )(f⋅g)(x)

Solve the equation. - 2(3x−7)=42 ^ { ( 3 x - 7 ) } = 42(3x−7)=4

Find the value of the logarithmic expression. - 8log⁡8158 ^ { \log _ { 8 } 15 }8log8​15

Graph the inverse of the function on the same set of axes. -

Graph the exponential function. - f(x)=3xf(x)=3^{x}f(x)=3x

Solve the equation. - log⁡37−log⁡3x=3\log _ { 3 } 7 - \log _ { 3 } x = 3log3​7−log3​x=3

Approximate the logarithm to four decimal places using the change of base formula. - log⁡25\log _ { 2 } 5log2​5

Graph the inverse of the function on the same set of axes. -

Provide an appropriate response. -Approximate log⁡59\log _ { 5 } 9log5​9 to four decimal places.

Solve for x. - log⁡X36=2\log _ { \mathrm { X } } 36 = 2logX​36=2

Solve. Round the answer to the nearest whole. -The size of the coyote population at a national park increases at the rate of 4.4% per year. If the size of the current population is 140, find how many coyotes there will be in 7 years.

For the given functions f and g, find the composition. - f(x)=x+3;g(x)=2xf ( x ) = \sqrt { x + 3 } ; g ( x ) = 2 xf(x)=x+3​;g(x)=2x Find (f∘g)(2)( f \circ g ) ( 2 )(f∘g)(2) .

Determine whether the function is a one-to-one function. - f={(−8,−6),(−18,−6),(−5,8)}f = \{ ( - 8 , - 6 ) , ( - 18 , - 6 ) , ( - 5,8 ) \}f={(−8,−6),(−18,−6),(−5,8)}

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

Find the exact value. - $\log 100$

Solve the equation. Give an approximate solution to four decimal places. - $\mathrm { e } ^ { 2 \mathrm { x } } = 7$

Provide an appropriate response. -If $f ( x ) = x , g ( x ) = x - 1$ , and $h ( x ) = x ^ { 2 } - 5 x + 5$ , find the composition $( g \circ f ) ( x )$ .

Provide an appropriate response. -If $f ( x ) = x$ and $g ( x ) = 7 x - 5$ , find $( f - g ) ( x )$

f(x)=4 x-1 ; g(x)=6 x-2 Find $( f \cdot g ) ( x )$

Solve the equation. - $2 ^ { ( 3 x - 7 ) } = 4$

Find the value of the logarithmic expression. - $8 ^ { \log _ { 8 } 15 }$

Graph the exponential function. - $f(x)=3^{x}$ $Graph the exponential function. - f(x)=3^{x}$

Solve the equation. - $\log _ { 3 } 7 - \log _ { 3 } x = 3$

Approximate the logarithm to four decimal places using the change of base formula. - $\log _ { 2 } 5$

Provide an appropriate response. -Approximate $\log _ { 5 } 9$ to four decimal places.

Solve for x. - $\log _ { \mathrm { X } } 36 = 2$

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

Determine whether the function is a one-to-one function. - $f = \{ ( - 8 , - 6 ) , ( - 18 , - 6 ) , ( - 5,8 ) \}$