Question 1

If $f ( x ) = x + 2$ and $g ( x ) = 3 x ^ { 2 } + 7 x$, find $( g \circ f ) ( x )$

Accepted Answer

A)  $( g \circ f ) ( x ) = 3 x ^ { 2 } + 19 x + 26$ 
B)  $( g \circ f ) ( x ) = 3 x ^ { 2 } + 7 x + 2$ 
C)  $( g \circ f ) ( x ) = 3 x ^ { 2 } + 19 x + 2$ 
D)  $( g \circ f ) ( x ) = 3 x ^ { 2 } + 7 x + 26$ 
A)  $( g \circ f ) ( x ) = 3 x ^ { 2 } + 19 x + 26$ 
B)  $( g \circ f ) ( x ) = 3 x ^ { 2 } + 7 x + 2$ 
C)  $( g \circ f ) ( x ) = 3 x ^ { 2 } + 19 x + 2$ 
D)  $( g \circ f ) ( x ) = 3 x ^ { 2 } + 7 x + 26$

Question 2

Expand into sums and/or differences of logarithms. Assume all variables represent positive real numbers. $\log _ { 1 / 2 } ( a b c )$

Accepted Answer

A)  $\frac { 1 } { 2 } \log a + \frac { 1 } { 2 } \log b + \frac { 1 } { 2 } \log c$ 
B)  $\left( \log _ { 1 / 2 } a \right) \left( \log _ { 1 / 2 } b \right) \left( \log _ { 1 / 2 } c \right)$ 
C)  $\log _ { 1 / 2 } a - \log _ { 1 / 2 } b - \log _ { 1 / 2 } c$ 
D)  $\log _ { 1 / 2 } a + \log _ { 1 / 2 } b + \log _ { 1 / 2 } c$ 
A)  $\frac { 1 } { 2 } \log a + \frac { 1 } { 2 } \log b + \frac { 1 } { 2 } \log c$ 
B)  $\left( \log _ { 1 / 2 } a \right) \left( \log _ { 1 / 2 } b \right) \left( \log _ { 1 / 2 } c \right)$ 
C)  $\log _ { 1 / 2 } a - \log _ { 1 / 2 } b - \log _ { 1 / 2 } c$ 
D)  $\log _ { 1 / 2 } a + \log _ { 1 / 2 } b + \log _ { 1 / 2 } c$

Question 3

Solve the exponential equation by taking the logarithm of both sides. $4 ^ { x + 6 } = 9 ^ { x }$

Accepted Answer

A)  $\left\{ \frac { 6 } { 1 - \ln 9 } \right\}$ 
B)  $\left\{ \frac { 6 \ln 4 } { \ln 4 - \ln 9 } \right\}$ 
C)  $\left\{ \frac { 6 } { \ln 9 - 1 } \right\}$ 
D)  $\left\{ \frac { 6 \ln 4 } { \ln 9 - \ln 4 } \right\}$ 
A)  $\left\{ \frac { 6 } { 1 - \ln 9 } \right\}$ 
B)  $\left\{ \frac { 6 \ln 4 } { \ln 4 - \ln 9 } \right\}$ 
C)  $\left\{ \frac { 6 } { \ln 9 - 1 } \right\}$ 
D)  $\left\{ \frac { 6 \ln 4 } { \ln 9 - \ln 4 } \right\}$

Question 4

Evaluate the expression by using a calculator. Round to 4 decimal places. $4 \sqrt { 3 }$

Accepted Answer

A)  9.0827 
B)  8.0000 
C)  14.2457 
D)  11.0357 
A)  9.0827 
B)  8.0000 
C)  14.2457 
D)  11.0357

Question 5

Scientists often use a process called carbon dating to estimate the age of archaeological finds. The process measures the amount of carbon-14, a radioactive isotope with a half-life of 5,730 years. If a Sample of wood from an ancient artifact had 12 grams of carbon-14 initially, the amount remaining, in Grams, is given by $A ( t ) = 12 \left( \frac { 1 } { 2 } \right) ^ { t / 5,730 }$ where t is the number of years since the tree died. How many grams would be present after 5,730 Years?

Accepted Answer

A)  3 g 
B)  24 g 
C)  0.27 g 
D)  6 g 
A)  3 g 
B)  24 g 
C)  0.27 g 
D)  6 g

Question 6

The cost in dollars of producing x toy cars is C(x) = 1.8x + 2. The revenue for selling x toy cars is R(x) = 6.08x. To calculate profit, subtract the cost from the revenue.
a. Write and simplify a function P that represents profit in terms of x.
b. Find the profit of producing 50 toy cars.

Accepted Answer

a. P(x) =

Question 7

If $m ( x ) = x ^ { 3 }$ and $n ( x ) = \sqrt { 6 + x }$ find the function value, if possible.
$\left( \frac { m } { n } \right) ( - 6 )$

Accepted Answer

A)  $- \frac { 108 } { \sqrt { 3 } }$ 
B)  $- 216$ 
C)  0 
D)  Undefined 
A)  $- \frac { 108 } { \sqrt { 3 } }$ 
B)  $- 216$ 
C)  0 
D)  Undefined

Question 8

Write an equation of the inverse for the one-to-one function $$g ( x ) = x ^ { 2 } + 4 \text { where } x \geq 0$$

Accepted Answer

A)  $g ^ { - 1 } ( x ) = \sqrt { x } - 2$ 
B)  $g ^ { - 1 } ( x ) = \sqrt { x - 4 }$ 
C)  $g ^ { - 1 } ( x ) = g ^ { - 1 } ( x ) = \sqrt { x + 4 }$ 
D)  $g ^ { - 1 } ( x ) = \sqrt { x } + 2$ 
A)  $g ^ { - 1 } ( x ) = \sqrt { x } - 2$ 
B)  $g ^ { - 1 } ( x ) = \sqrt { x - 4 }$ 
C)  $g ^ { - 1 } ( x ) = g ^ { - 1 } ( x ) = \sqrt { x + 4 }$ 
D)  $g ^ { - 1 } ( x ) = \sqrt { x } + 2$

Question 9

Evaluate the expression. $\log _ { 1 / 3 } \left( \frac { 1 } { 3 } \right) ^ { 5 }$

Accepted Answer

A)  $\frac { 1 } { 243 }$ 
B)  $- 5$ 
C)  $\frac { 5 } { 3 }$ 
D)  5 
A)  $\frac { 1 } { 243 }$ 
B)  $- 5$ 
C)  $\frac { 5 } { 3 }$ 
D)  5

Question 10

Find the domain of the function and express the domain in interval notation. $$g ( x ) = \log _ { 5 } x$$

Accepted Answer

A)  $( 5 , \infty )$ 
B)  $( - \infty , \infty )$ 
C)  $[ 0 , \infty )$ 
D)  $( 0 , \infty )$ 
A)  $( 5 , \infty )$ 
B)  $( - \infty , \infty )$ 
C)  $[ 0 , \infty )$ 
D)  $( 0 , \infty )$

Question 11

Solve the exponential equation by taking the logarithm of both sides. $11 - 4 ^ { x ^ { 2 } } = 3$

Accepted Answer

A)  $\left\{ \frac { \sqrt { \ln x } } { 4 } \right\}$ 
B)  $\left\{ - \frac { \sqrt { 6 } } { 2 } , \frac { \sqrt { 6 } } { 2 } \right\}$ 
C)  $\{ - \sqrt { \ln x } , \sqrt { \ln x } \}$ 
D)  $\{ \sqrt { 2 } , - \sqrt { 2 } \}$ 
A)  $\left\{ \frac { \sqrt { \ln x } } { 4 } \right\}$ 
B)  $\left\{ - \frac { \sqrt { 6 } } { 2 } , \frac { \sqrt { 6 } } { 2 } \right\}$ 
C)  $\{ - \sqrt { \ln x } , \sqrt { \ln x } \}$ 
D)  $\{ \sqrt { 2 } , - \sqrt { 2 } \}$

Question 12

Evaluate without the use of a calculator. $\log 10 ^ { 5 }$

Accepted Answer

A)  5 
B)  50 
C)  $5 ^ { 10 }$ 
D)  $- 5$ 
A)  5 
B)  50 
C)  $5 ^ { 10 }$ 
D)  $- 5$

Question 13

Solve the logarithmic equation. $$\log _ { 1 / 3 } ( 2 z + 5 ) - \log _ { 1 / 3 } z = - 3$$

Accepted Answer

A)  $\left\{ \frac { 11 } { 3 } \right\}$ 
B) {  } 
C)  $\{ 9 \}$ 
D)  $\left\{ \frac { 1 } { 5 } \right\}$ 
A)  $\left\{ \frac { 11 } { 3 } \right\}$ 
B) {  } 
C)  $\{ 9 \}$ 
D)  $\left\{ \frac { 1 } { 5 } \right\}$

Question 14

Expand into a sum and/or difference of logarithms. Assume all variables represent positive real numbers. $$\log _ { 12 } ( x y )$$

Accepted Answer

A)  $\left( \log _ { 12 } x \right) \cdot y$ 
B)  $\log _ { 12 } x \times \log _ { 12 } y$ 
C)  $\log _ { 12 } x + \log _ { 12 } y$ 
D)  $\log _ { 12 } x - \log _ { 12 } y$ 
A)  $\left( \log _ { 12 } x \right) \cdot y$ 
B)  $\log _ { 12 } x \times \log _ { 12 } y$ 
C)  $\log _ { 12 } x + \log _ { 12 } y$ 
D)  $\log _ { 12 } x - \log _ { 12 } y$

Question 15

Write the equation in exponential form. $$\log _ { 3 } \frac { 1 } { 729 } = - 6$$

Accepted Answer

The answer of Write the equation in exponential form. \[\log...

Question 16

If $f ( x ) = 11 x + 7$ and $g ( x ) = x ^ { 2 } - 2 x$, find $( f \circ g ) ( x )$.

Accepted Answer

A)  $( f \circ g ) ( x ) = 11 x ^ { 2 } - 22 x + 7$ 
B)  $( f \circ g ) ( x ) = x ^ { 2 } + 9 x + 7$ 
C)  $( f \circ g ) ( x ) = 11 x ^ { 3 } - 15 x ^ { 2 } - 14 x$ 
D)  $( f \circ g ) ( x ) = x ^ { 2 } + 13 x + 7$ 
A)  $( f \circ g ) ( x ) = 11 x ^ { 2 } - 22 x + 7$ 
B)  $( f \circ g ) ( x ) = x ^ { 2 } + 9 x + 7$ 
C)  $( f \circ g ) ( x ) = 11 x ^ { 3 } - 15 x ^ { 2 } - 14 x$ 
D)  $( f \circ g ) ( x ) = x ^ { 2 } + 13 x + 7$

Question 17

Evaluate the expression. $13 ^ { \log _ { 13 } 11 }$

Accepted Answer

A)  24 
B)  143 
C)  13 
D)  11 
A)  24 
B)  143 
C)  13 
D)  11

Question 18

Evaluate the expression. $$\log _ { 2 } 2 + \log _ { 13 } 1$$

Accepted Answer

A)  1 
B)  3 
C)  $\log _ { 13 } 3$ 
D)  2 
A)  1 
B)  3 
C)  $\log _ { 13 } 3$ 
D)  2

Question 19

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

Accepted Answer

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

Question 20

Write the inverse function for $f = \{ ( - 3,5 ) , ( - 7,9 ) , ( 4 , - 9 ) , ( - 5 , - 3 ) \}$.

Accepted Answer

A)  $f ^ { - 1 } = \{ ( 5 , - 3 ) , ( 9 , - 7 ) , ( - 9,4 ) , ( - 3 , - 5 ) \}$ 
B)  $f ^ { - 1 } = \{ ( - 5,3 ) , ( - 9,7 ) , ( 9 , - 4 ) , ( 3,5 ) \}$ 
C)  $f ^ { - 1 } = \{ ( 3 , - 5 ) , ( 7 , - 9 ) , ( - 4,9 ) , ( 5,3 ) \}$ 
D)  $f ^ { - 1 } = \left\{ \left( - \frac { 1 } { 3 } , \frac { 1 } { 5 } \right) , \left( - \frac { 1 } { 7 } , \frac { 1 } { 9 } \right) , \left( \frac { 1 } { 4 } , - \frac { 1 } { 9 } \right) , \left( - \frac { 1 } { 5 } , - \frac { 1 } { 3 } \right) \right\}$ 
A)  $f ^ { - 1 } = \{ ( 5 , - 3 ) , ( 9 , - 7 ) , ( - 9,4 ) , ( - 3 , - 5 ) \}$ 
B)  $f ^ { - 1 } = \{ ( - 5,3 ) , ( - 9,7 ) , ( 9 , - 4 ) , ( 3,5 ) \}$ 
C)  $f ^ { - 1 } = \{ ( 3 , - 5 ) , ( 7 , - 9 ) , ( - 4,9 ) , ( 5,3 ) \}$ 
D)  $f ^ { - 1 } = \left\{ \left( - \frac { 1 } { 3 } , \frac { 1 } { 5 } \right) , \left( - \frac { 1 } { 7 } , \frac { 1 } { 9 } \right) , \left( \frac { 1 } { 4 } , - \frac { 1 } { 9 } \right) , \left( - \frac { 1 } { 5 } , - \frac { 1 } { 3 } \right) \right\}$

If $f ( x ) = x + 2$ and $g ( x ) = 3 x ^ { 2 } + 7 x$ , find $( g \circ f ) ( x )$

Expand into sums and/or differences of logarithms. Assume all variables represent positive real numbers. $\log _ { 1 / 2 } ( a b c )$

Solve the exponential equation by taking the logarithm of both sides. $4 ^ { x + 6 } = 9 ^ { x }$

Evaluate the expression by using a calculator. Round to 4 decimal places. $4 \sqrt { 3 }$

The cost in dollars of producing x toy cars is C(x) = 1.8x + 2. The revenue for selling x toy cars is R(x) = 6.08x. To calculate profit, subtract the cost from the revenue. a. Write and simplify a function P that represents profit in terms of x. b. Find the profit of producing 50 toy cars.

If $m ( x ) = x ^ { 3 }$ and $n ( x ) = \sqrt { 6 + x }$ find the function value, if possible. $\left( \frac { m } { n } \right) ( - 6 )$

Write an equation of the inverse for the one-to-one function $g ( x ) = x ^ { 2 } + 4 \text { where } x \geq 0$

Evaluate the expression. $\log _ { 1 / 3 } \left( \frac { 1 } { 3 } \right) ^ { 5 }$

Find the domain of the function and express the domain in interval notation. $g ( x ) = \log _ { 5 } x$

Solve the exponential equation by taking the logarithm of both sides. $11 - 4 ^ { x ^ { 2 } } = 3$

Evaluate without the use of a calculator. $\log 10 ^ { 5 }$

Solve the logarithmic equation. $\log _ { 1 / 3 } ( 2 z + 5 ) - \log _ { 1 / 3 } z = - 3$

Expand into a sum and/or difference of logarithms. Assume all variables represent positive real numbers. $\log _ { 12 } ( x y )$

Write the equation in exponential form. $\log _ { 3 } \frac { 1 } { 729 } = - 6$

If $f ( x ) = 11 x + 7$ and $g ( x ) = x ^ { 2 } - 2 x$ , find $( f \circ g ) ( x )$ .

Evaluate the expression. $13 ^ { \log _ { 13 } 11 }$

Evaluate the expression. $\log _ { 2 } 2 + \log _ { 13 } 1$

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

Write the inverse function for $f = \{ ( - 3,5 ) , ( - 7,9 ) , ( 4 , - 9 ) , ( - 5 , - 3 ) \}$ .

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Polynomials

Rational Expressions and Rational Equations

Radicals and Complex Numbers

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Exam 8: Exponential and Logarithmic Functions and Applications

If f(x)=x+2f ( x ) = x + 2f(x)=x+2 and g(x)=3x2+7xg ( x ) = 3 x ^ { 2 } + 7 xg(x)=3x2+7x , find (g∘f)(x)( g \circ f ) ( x )(g∘f)(x)

Expand into sums and/or differences of logarithms. Assume all variables represent positive real numbers. log⁡1/2(abc)\log _ { 1 / 2 } ( a b c )log1/2​(abc)

Solve the exponential equation by taking the logarithm of both sides. 4x+6=9x4 ^ { x + 6 } = 9 ^ { x }4x+6=9x

Evaluate the expression by using a calculator. Round to 4 decimal places. 434 \sqrt { 3 }43​

The cost in dollars of producing x toy cars is C(x) = 1.8x + 2. The revenue for selling x toy cars is R(x) = 6.08x. To calculate profit, subtract the cost from the revenue. a. Write and simplify a function P that represents profit in terms of x. b. Find the profit of producing 50 toy cars.

If m(x)=x3m ( x ) = x ^ { 3 }m(x)=x3 and n(x)=6+xn ( x ) = \sqrt { 6 + x }n(x)=6+x​ find the function value, if possible. (mn)(−6)\left( \frac { m } { n } \right) ( - 6 )(nm​)(−6)

Write an equation of the inverse for the one-to-one function g(x)=x2+4 where x≥0g ( x ) = x ^ { 2 } + 4 \text { where } x \geq 0g(x)=x2+4 where x≥0

Evaluate the expression. log⁡1/3(13)5\log _ { 1 / 3 } \left( \frac { 1 } { 3 } \right) ^ { 5 }log1/3​(31​)5

Find the domain of the function and express the domain in interval notation. g(x)=log⁡5xg ( x ) = \log _ { 5 } xg(x)=log5​x

Solve the exponential equation by taking the logarithm of both sides. 11−4x2=311 - 4 ^ { x ^ { 2 } } = 311−4x2=3

Evaluate without the use of a calculator. log⁡105\log 10 ^ { 5 }log105

Solve the logarithmic equation. log⁡1/3(2z+5)−log⁡1/3z=−3\log _ { 1 / 3 } ( 2 z + 5 ) - \log _ { 1 / 3 } z = - 3log1/3​(2z+5)−log1/3​z=−3

Expand into a sum and/or difference of logarithms. Assume all variables represent positive real numbers. log⁡12(xy)\log _ { 12 } ( x y )log12​(xy)

Write the equation in exponential form. log⁡31729=−6\log _ { 3 } \frac { 1 } { 729 } = - 6log3​7291​=−6

If f(x)=11x+7f ( x ) = 11 x + 7f(x)=11x+7 and g(x)=x2−2xg ( x ) = x ^ { 2 } - 2 xg(x)=x2−2x , find (f∘g)(x)( f \circ g ) ( x )(f∘g)(x) .

Evaluate the expression. 13log⁡131113 ^ { \log _ { 13 } 11 }13log13​11

Evaluate the expression. log⁡22+log⁡131\log _ { 2 } 2 + \log _ { 13 } 1log2​2+log13​1

Graph the function f(x)=(12)xf ( x ) = \left( \frac { 1 } { 2 } \right) ^ { x }f(x)=(21​)x

Write the inverse function for f={(−3,5),(−7,9),(4,−9),(−5,−3)}f = \{ ( - 3,5 ) , ( - 7,9 ) , ( 4 , - 9 ) , ( - 5 , - 3 ) \}f={(−3,5),(−7,9),(4,−9),(−5,−3)} .

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Polynomials

Rational Expressions and Rational Equations

Radicals and Complex Numbers

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Online: Transformations, Piecewise-Defined Functions, and Probability

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If $f ( x ) = x + 2$ and $g ( x ) = 3 x ^ { 2 } + 7 x$ , find $( g \circ f ) ( x )$

Expand into sums and/or differences of logarithms. Assume all variables represent positive real numbers. $\log _ { 1 / 2 } ( a b c )$

Solve the exponential equation by taking the logarithm of both sides. $4 ^ { x + 6 } = 9 ^ { x }$

Evaluate the expression by using a calculator. Round to 4 decimal places. $4 \sqrt { 3 }$

If $m ( x ) = x ^ { 3 }$ and $n ( x ) = \sqrt { 6 + x }$ find the function value, if possible. $\left( \frac { m } { n } \right) ( - 6 )$

Write an equation of the inverse for the one-to-one function $g ( x ) = x ^ { 2 } + 4 \text { where } x \geq 0$

Evaluate the expression. $\log _ { 1 / 3 } \left( \frac { 1 } { 3 } \right) ^ { 5 }$

Find the domain of the function and express the domain in interval notation. $g ( x ) = \log _ { 5 } x$

Solve the exponential equation by taking the logarithm of both sides. $11 - 4 ^ { x ^ { 2 } } = 3$

Evaluate without the use of a calculator. $\log 10 ^ { 5 }$

Solve the logarithmic equation. $\log _ { 1 / 3 } ( 2 z + 5 ) - \log _ { 1 / 3 } z = - 3$

Expand into a sum and/or difference of logarithms. Assume all variables represent positive real numbers. $\log _ { 12 } ( x y )$

Write the equation in exponential form. $\log _ { 3 } \frac { 1 } { 729 } = - 6$

If $f ( x ) = 11 x + 7$ and $g ( x ) = x ^ { 2 } - 2 x$ , find $( f \circ g ) ( x )$ .

Evaluate the expression. $13 ^ { \log _ { 13 } 11 }$

Evaluate the expression. $\log _ { 2 } 2 + \log _ { 13 } 1$

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

Write the inverse function for $f = \{ ( - 3,5 ) , ( - 7,9 ) , ( 4 , - 9 ) , ( - 5 , - 3 ) \}$ .