Question 1

Use a calculator to approximate the logarithm to four decimal places.
-$\log 194$

Accepted Answer

A)  $2.2856$ 
B)  $5.2679$ 
C)  $2.2900$ 
D)  $2.2878$ 
A)  $2.2856$ 
B)  $5.2679$ 
C)  $2.2900$ 
D)  $2.2878$

Question 2

Solve the equation.
-$3 ^ { 3 x } = \frac { 1 } { 9 }$

Accepted Answer

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

Question 3

Express as the logarithm of a single expression. Assume that variables represent positive numbers.
-$\log _ { 5 } 9 - \log _ { 5 } 10$

Accepted Answer

A)  $\log _ { 10 } \frac { 9 } { 10 }$ 
B)  $\log _ { 5 } - 1$ 
C)  $\log _ { 5 } \frac { 10 } { 9 }$ 
D)  $\log _ { 5 } \frac { 9 } { 10 }$ 
A)  $\log _ { 10 } \frac { 9 } { 10 }$ 
B)  $\log _ { 5 } - 1$ 
C)  $\log _ { 5 } \frac { 10 } { 9 }$ 
D)  $\log _ { 5 } \frac { 9 } { 10 }$

Question 4

If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs.
-$f = \{ ( 6,1 ) , ( - 4,2 ) , ( - 6,3 ) , ( - 8,4 ) \}$

Accepted Answer

A)  $f ^ { - 1 } = \{ ( 1,6 ) , ( 2 , - 4 ) , ( 3 , - 6 ) , ( 4 , - 8 ) \}$ 
B)  not one-to-one 
C)  $f ^ { - 1 } = \{ ( 2,1 ) , ( 4 , - 6 ) , ( 6 , - 6 ) , ( 2,3 ) \}$ 
D)  $f ^ { - 1 } = \{ ( 2,1 ) , ( 1 , - 6 ) , ( 6 , - 4 ) , ( 2,3 ) \}$ 
A)  $f ^ { - 1 } = \{ ( 1,6 ) , ( 2 , - 4 ) , ( 3 , - 6 ) , ( 4 , - 8 ) \}$ 
B)  not one-to-one 
C)  $f ^ { - 1 } = \{ ( 2,1 ) , ( 4 , - 6 ) , ( 6 , - 6 ) , ( 2,3 ) \}$ 
D)  $f ^ { - 1 } = \{ ( 2,1 ) , ( 1 , - 6 ) , ( 6 , - 4 ) , ( 2,3 ) \}$

Question 5

For the given functions f and g, find the requested function.
-$f ( x ) = x - 5 ; g ( x ) = 8 x ^ { 2 } \quad$ Find $( f - g ) ( x )$

Accepted Answer

A)  $( f - g ) ( x ) = 8 x ^ { 2 } - x + 5$ 
B)  $( f - g ) ( x ) = 8 x ^ { 2 } + x - 5$ 
C)  $( f - g ) ( x ) = - 8 x ^ { 2 } + x - 5$ 
D)  $( f - g ) ( x ) = - 8 x ^ { 2 } - x - 5$ 
A)  $( f - g ) ( x ) = 8 x ^ { 2 } - x + 5$ 
B)  $( f - g ) ( x ) = 8 x ^ { 2 } + x - 5$ 
C)  $( f - g ) ( x ) = - 8 x ^ { 2 } + x - 5$ 
D)  $( f - g ) ( x ) = - 8 x ^ { 2 } - x - 5$

Question 6

Solve the equation for x. Give an exact solution.
-$\ln ( 13 x + 5 ) = - 0.5$

Accepted Answer

A)  $13 \left( e ^ { - 0.5 } - 5 \right)$ 
B)  $\frac { e ^ { - 0.5 } + 13 } { 5 }$ 
C)  $\frac { e ^ { - 0.5 } - 5 } { 13 }$ 
D)  $\mathrm { e } ^ { - 0.5 } - 5$ 
A)  $13 \left( e ^ { - 0.5 } - 5 \right)$ 
B)  $\frac { e ^ { - 0.5 } + 13 } { 5 }$ 
C)  $\frac { e ^ { - 0.5 } - 5 } { 13 }$ 
D)  $\mathrm { e } ^ { - 0.5 } - 5$

Question 7

Solve for x.
-$\log _ { 5 } \frac { 1 } { 25 } = x$

Accepted Answer

A)  $\frac { 1 } { 125 }$ 
B)  2 
C)  $- 2$ 
D)  $\frac { 1 } { 5 }$ 
A)  $\frac { 1 } { 125 }$ 
B)  2 
C)  $- 2$ 
D)  $\frac { 1 } { 5 }$

Question 8

If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs.
-$f = \{ ( 6,2 ) , ( - 6 , - 2 ) , ( 6,0 ) , ( - 6,0 ) \}$

Accepted Answer

A)  $f ^ { - 1 } = \{ ( 2,6 ) , ( - 2 , - 6 ) , ( 0,6 ) , ( 0 , - 6 ) \}$ 
B)  $f ^ { - 1 } = \{ ( 2,6 ) , ( 6 , - 6 ) , ( 0,6 ) , ( 0 , - 6 ) \}$ 
C)  not one-to-one 
D)  $f ^ { - 1 } = \{ ( 2,6 ) , ( - 2 , - 6 ) , ( 0 , - 6 ) , ( 0 , - 6 ) \}$ 
A)  $f ^ { - 1 } = \{ ( 2,6 ) , ( - 2 , - 6 ) , ( 0,6 ) , ( 0 , - 6 ) \}$ 
B)  $f ^ { - 1 } = \{ ( 2,6 ) , ( 6 , - 6 ) , ( 0,6 ) , ( 0 , - 6 ) \}$ 
C)  not one-to-one 
D)  $f ^ { - 1 } = \{ ( 2,6 ) , ( - 2 , - 6 ) , ( 0 , - 6 ) , ( 0 , - 6 ) \}$

Question 9

Graph the exponential function.
-$f(x)=\left(\frac{1}{5}\right)^{|x|}$

Accepted Answer

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

Question 10

Graph the exponential function.
-$f(x)=\left(\frac{1}{5}\right)^{x}$

Accepted Answer

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

Question 11

On the same set of axes, graph the given one-to-one function and its inverse .
-$f(x)=-2 x+1$

Accepted Answer

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

Question 12

Use the exponential growth formula to find the final amount. Round to the nearest whole.
-

Accepted Answer

A)  985,261 
B)  879,360 
C)  $2,193,346$ 
D)  784,240 
A)  985,261 
B)  879,360 
C)  $2,193,346$ 
D)  784,240

Question 13

For the given functions f and g, find the requested function.
-$f ( x ) = \sqrt { 2 x } ; g ( x ) = - 3 x + 7 \quad$ Find $( f \cdot g ) ( x )$

Accepted Answer

A)  $( f \cdot g ) ( x ) = - 6 x + 7 \sqrt { 2 x }$ 
B)  $( f \cdot g ) ( x ) = - 3 x \sqrt { 2 x } + 7 \sqrt { 2 x }$ 
C)  $( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = - 6 \mathrm { x } ^ { 2 } + 14$ 
D)  $( f \cdot g ) ( x ) = \sqrt { 2 x } + 21 x$ 
A)  $( f \cdot g ) ( x ) = - 6 x + 7 \sqrt { 2 x }$ 
B)  $( f \cdot g ) ( x ) = - 3 x \sqrt { 2 x } + 7 \sqrt { 2 x }$ 
C)  $( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = - 6 \mathrm { x } ^ { 2 } + 14$ 
D)  $( f \cdot g ) ( x ) = \sqrt { 2 x } + 21 x$

Question 14

For the given functions f and g, find the composition.
-$f ( x ) = x ^ { 3 } - 4 x ; g ( x ) = 2 x \quad$ Find $( f \circ g ) ( x )$.

Accepted Answer

A)  $8 x ^ { 3 } - 8 x$ 
B)  $8 x ^ { 2 } - 8 x$ 
C)  $2 x ^ { 3 } - 8 x$ 
D)  $2 x ^ { 3 } - 4 x$ 
A)  $8 x ^ { 3 } - 8 x$ 
B)  $8 x ^ { 2 } - 8 x$ 
C)  $2 x ^ { 3 } - 8 x$ 
D)  $2 x ^ { 3 } - 4 x$

Question 15

Use the exponential growth formula to find the final amount. Round to the nearest whole.
-

Accepted Answer

A)  701 
B)  655 
C)  228 
D)  699 
A)  701 
B)  655 
C)  228 
D)  699

Question 16

Solve the equation. Give an exact solution.
-$\mathrm { e } ^ { 2 \mathrm { x } } = 5$

Accepted Answer

A)  $2 \ln 5$ 
B)  $\frac { 5 } { 2 } \mathrm { e }$ 
C)  $\frac { \ln 5 } { 2 }$ 
D)  $\frac { \ln 2 } { 5 }$ 
A)  $2 \ln 5$ 
B)  $\frac { 5 } { 2 } \mathrm { e }$ 
C)  $\frac { \ln 5 } { 2 }$ 
D)  $\frac { \ln 2 } { 5 }$

Question 17

For the given functions f and g, find the requested function.
-If $f ( x ) = 7 x + 6$ and $g ( x ) = 3 x - 1$, find (f $g ) ( x )$.

Accepted Answer

A)  $21 x - 1$ 
B)  $21 x + 5$ 
C)  $21 x + 13$ 
D)  $21 \mathrm { x } + 17$ 
A)  $21 x - 1$ 
B)  $21 x + 5$ 
C)  $21 x + 13$ 
D)  $21 \mathrm { x } + 17$

Question 18

Solve.
-The population in a particular country is growing at the rate of $1.3 \%$ per year. If $3,819,000$ people live there currently, how many will be there 5 years from now? Use $\mathrm { y } ^ { - } \mathrm { y } _ { 0 } \mathrm { e } ^ { 0.013 \mathrm { t } }$ and round to the nearest ten-thousand.

Accepted Answer

A)  $3,990,000$ 
B)  $4,480,000$ 
C)  $4,890,000$ 
D)  $4,080,000$ 
A)  $3,990,000$ 
B)  $4,480,000$ 
C)  $4,890,000$ 
D)  $4,080,000$

Question 19

Write the function F(x) as a composition of f, g, or h.
-$\begin{array} { l } 
f ( x ) = x ^ { 2 } - 6 \quad g ( x ) = 4 x \quad h ( x ) = \sqrt { x - 7 } \
F ( x ) = \sqrt { 4 x - 7 }
\end{array}$

Accepted Answer

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

Question 20

For the given functions f and g, find the requested function.
-$f ( x ) = 2 x ^ { 3 } - 1 ; g ( x ) = 4 x ^ { 2 } - 1 \quad$ Find $( f \cdot g ) ( x )$.

Accepted Answer

A)  $( f \cdot g ) ( x ) = 2 x ^ { 3 } + 4 x ^ { 2 } + 1$ 
B)  $( f \cdot g ) ( x ) = 8 x ^ { 5 } - 2 x ^ { 3 } - 4 x ^ { 2 } + 1$ 
C)  $( f \cdot g ) ( x ) = 8 x ^ { 6 } - 2 x ^ { 3 } - 4 x ^ { 2 } + 1$ 
D)  $( f \cdot g ) ( x ) = - 8 x ^ { 5 } - 2 x ^ { 3 } - 4 x ^ { 2 } + 1$ 
A)  $( f \cdot g ) ( x ) = 2 x ^ { 3 } + 4 x ^ { 2 } + 1$ 
B)  $( f \cdot g ) ( x ) = 8 x ^ { 5 } - 2 x ^ { 3 } - 4 x ^ { 2 } + 1$ 
C)  $( f \cdot g ) ( x ) = 8 x ^ { 6 } - 2 x ^ { 3 } - 4 x ^ { 2 } + 1$ 
D)  $( f \cdot g ) ( x ) = - 8 x ^ { 5 } - 2 x ^ { 3 } - 4 x ^ { 2 } + 1$

Use a calculator to approximate the logarithm to four decimal places. - $\log 194$

Solve the equation. - $3 ^ { 3 x } = \frac { 1 } { 9 }$

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $\log _ { 5 } 9 - \log _ { 5 } 10$

If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs. - $f = \{ ( 6,1 ) , ( - 4,2 ) , ( - 6,3 ) , ( - 8,4 ) \}$

For the given functions f and g, find the requested function. - $f ( x ) = x - 5 ; g ( x ) = 8 x ^ { 2 } \quad$ Find $( f - g ) ( x )$

Solve the equation for x. Give an exact solution. - $\ln ( 13 x + 5 ) = - 0.5$

Solve for x. - $\log _ { 5 } \frac { 1 } { 25 } = x$

If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs. - $f = \{ ( 6,2 ) , ( - 6 , - 2 ) , ( 6,0 ) , ( - 6,0 ) \}$

Graph the exponential function. - $f(x)=\left(\frac{1}{5}\right)^{|x|}$ $Graph the exponential function. - f(x)=\left(\frac{1}{5}\right)^{|x|}$

Graph the exponential function. - $f(x)=\left(\frac{1}{5}\right)^{x}$ $Graph the exponential function. - f(x)=\left(\frac{1}{5}\right)^{x}$

On the same set of axes, graph the given one-to-one function and its inverse . - $f(x)=-2 x+1$

Use the exponential growth formula to find the final amount. Round to the nearest whole. -

For the given functions f and g, find the requested function. - $f ( x ) = \sqrt { 2 x } ; g ( x ) = - 3 x + 7 \quad$ Find $( f \cdot g ) ( x )$

For the given functions f and g, find the composition. - $f ( x ) = x ^ { 3 } - 4 x ; g ( x ) = 2 x \quad$ Find $( f \circ g ) ( x )$ .

Use the exponential growth formula to find the final amount. Round to the nearest whole. -

Solve the equation. Give an exact solution. - $\mathrm { e } ^ { 2 \mathrm { x } } = 5$

For the given functions f and g, find the requested function. -If $f ( x ) = 7 x + 6$ and $g ( x ) = 3 x - 1$ , find (f $g ) ( x )$ .

Write the function F(x) as a composition of f, g, or h. - f(x)=-6g(x)=4xh(x)= F(x)=

For the given functions f and g, find the requested function. - $f ( x ) = 2 x ^ { 3 } - 1 ; g ( x ) = 4 x ^ { 2 } - 1 \quad$ Find $( f \cdot g ) ( x )$ .

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

Use a calculator to approximate the logarithm to four decimal places. - log⁡194\log 194log194

Solve the equation. - 33x=193 ^ { 3 x } = \frac { 1 } { 9 }33x=91​

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - log⁡59−log⁡510\log _ { 5 } 9 - \log _ { 5 } 10log5​9−log5​10

If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs. - f={(6,1),(−4,2),(−6,3),(−8,4)}f = \{ ( 6,1 ) , ( - 4,2 ) , ( - 6,3 ) , ( - 8,4 ) \}f={(6,1),(−4,2),(−6,3),(−8,4)}

For the given functions f and g, find the requested function. - f(x)=x−5;g(x)=8x2f ( x ) = x - 5 ; g ( x ) = 8 x ^ { 2 } \quadf(x)=x−5;g(x)=8x2 Find (f−g)(x)( f - g ) ( x )(f−g)(x)

Solve the equation for x. Give an exact solution. - ln⁡(13x+5)=−0.5\ln ( 13 x + 5 ) = - 0.5ln(13x+5)=−0.5

Solve for x. - log⁡5125=x\log _ { 5 } \frac { 1 } { 25 } = xlog5​251​=x

If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs. - f={(6,2),(−6,−2),(6,0),(−6,0)}f = \{ ( 6,2 ) , ( - 6 , - 2 ) , ( 6,0 ) , ( - 6,0 ) \}f={(6,2),(−6,−2),(6,0),(−6,0)}

Graph the exponential function. - f(x)=(15)∣x∣f(x)=\left(\frac{1}{5}\right)^{|x|}f(x)=(51​)∣x∣

Graph the exponential function. - f(x)=(15)xf(x)=\left(\frac{1}{5}\right)^{x}f(x)=(51​)x

On the same set of axes, graph the given one-to-one function and its inverse . - f(x)=−2x+1f(x)=-2 x+1f(x)=−2x+1

Use the exponential growth formula to find the final amount. Round to the nearest whole. -

For the given functions f and g, find the requested function. - f(x)=2x;g(x)=−3x+7f ( x ) = \sqrt { 2 x } ; g ( x ) = - 3 x + 7 \quadf(x)=2x​;g(x)=−3x+7 Find (f⋅g)(x)( f \cdot g ) ( x )(f⋅g)(x)

For the given functions f and g, find the composition. - f(x)=x3−4x;g(x)=2xf ( x ) = x ^ { 3 } - 4 x ; g ( x ) = 2 x \quadf(x)=x3−4x;g(x)=2x Find (f∘g)(x)( f \circ g ) ( x )(f∘g)(x) .

Use the exponential growth formula to find the final amount. Round to the nearest whole. -

Solve the equation. Give an exact solution. - e2x=5\mathrm { e } ^ { 2 \mathrm { x } } = 5e2x=5

For the given functions f and g, find the requested function. -If f(x)=7x+6f ( x ) = 7 x + 6f(x)=7x+6 and g(x)=3x−1g ( x ) = 3 x - 1g(x)=3x−1 , find (f g)(x)g ) ( x )g)(x) .

Write the function F(x) as a composition of f, g, or h. - f(x)=-6g(x)=4xh(x)= F(x)=

For the given functions f and g, find the requested function. - f(x)=2x3−1;g(x)=4x2−1f ( x ) = 2 x ^ { 3 } - 1 ; g ( x ) = 4 x ^ { 2 } - 1 \quadf(x)=2x3−1;g(x)=4x2−1 Find (f⋅g)(x)( f \cdot g ) ( x )(f⋅g)(x) .

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

Use a calculator to approximate the logarithm to four decimal places. - $\log 194$

Solve the equation. - $3 ^ { 3 x } = \frac { 1 } { 9 }$

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $\log _ { 5 } 9 - \log _ { 5 } 10$

If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs. - $f = \{ ( 6,1 ) , ( - 4,2 ) , ( - 6,3 ) , ( - 8,4 ) \}$

For the given functions f and g, find the requested function. - $f ( x ) = x - 5 ; g ( x ) = 8 x ^ { 2 } \quad$ Find $( f - g ) ( x )$

Solve the equation for x. Give an exact solution. - $\ln ( 13 x + 5 ) = - 0.5$

Solve for x. - $\log _ { 5 } \frac { 1 } { 25 } = x$

If the function is one-to-one, list the inverse function by switching coordinates or inputs and outputs. - $f = \{ ( 6,2 ) , ( - 6 , - 2 ) , ( 6,0 ) , ( - 6,0 ) \}$

Graph the exponential function. - $f(x)=\left(\frac{1}{5}\right)^{|x|}$ $Graph the exponential function. - f(x)=\left(\frac{1}{5}\right)^{|x|}$

Graph the exponential function. - $f(x)=\left(\frac{1}{5}\right)^{x}$ $Graph the exponential function. - f(x)=\left(\frac{1}{5}\right)^{x}$

On the same set of axes, graph the given one-to-one function and its inverse . - $f(x)=-2 x+1$

For the given functions f and g, find the requested function. - $f ( x ) = \sqrt { 2 x } ; g ( x ) = - 3 x + 7 \quad$ Find $( f \cdot g ) ( x )$

For the given functions f and g, find the composition. - $f ( x ) = x ^ { 3 } - 4 x ; g ( x ) = 2 x \quad$ Find $( f \circ g ) ( x )$ .

Solve the equation. Give an exact solution. - $\mathrm { e } ^ { 2 \mathrm { x } } = 5$

For the given functions f and g, find the requested function. -If $f ( x ) = 7 x + 6$ and $g ( x ) = 3 x - 1$ , find (f $g ) ( x )$ .

For the given functions f and g, find the requested function. - $f ( x ) = 2 x ^ { 3 } - 1 ; g ( x ) = 4 x ^ { 2 } - 1 \quad$ Find $( f \cdot g ) ( x )$ .