Question 1

Evaluate the logarithm.
-$\log 100,000$

Accepted Answer

A)  1 
B)  $- 5$ 
C)  10 
D)  5 
A)  1 
B)  $- 5$ 
C)  10 
D)  5

Question 2

Use the product, quotient, and power rules of logarithms to rewrite the expression as a single logarithm. Assume that all
variables represent positive real numbers.
-$\log _ { 2 } 12 - \log _ { 2 } y$

Accepted Answer

A)  $\log _ { 2 } y / 12$ 
B)  $\log _ { 4 } 12 / y$ 
C)  $\log _ { 2 } 12 / \mathrm { y }$ 
D)  $\log _ { 2 } ( 12 - y )$ 
A)  $\log _ { 2 } y / 12$ 
B)  $\log _ { 4 } 12 / y$ 
C)  $\log _ { 2 } 12 / \mathrm { y }$ 
D)  $\log _ { 2 } ( 12 - y )$

Question 3

Graph the function. Describe its position relative to the graph of the indicated basic function.
-$$f ( x ) = 1 - 6 ^ { - x } ; \text { relative to } f ( x ) = 6 ^ { x }$$

Accepted Answer

A)  Reflected across y-axis;
reflected across x-axis;
moved up 1 unit(s)
  
B)  Moved up 1 unit(s);
reflected across, y-axis;
reflected across $x$-axis;
  
C)  Reflected across y-axis;
reflected across $x$-axis;
moved down 1 unit(s)
  
D)  Moved up 1 unit(s);
reflected across, y-axis;
reflected across $x$-axis;
  
A)  Reflected across y-axis;
reflected across x-axis;
moved up 1 unit(s)
  
B)  Moved up 1 unit(s);
reflected across, y-axis;
reflected across $x$-axis;
  
C)  Reflected across y-axis;
reflected across $x$-axis;
moved down 1 unit(s)
  
D)  Moved up 1 unit(s);
reflected across, y-axis;
reflected across $x$-axis;

Question 4

Describe how to transform the graph of the basic function g(x) into the graph of the given function f(x).
-$$f ( x ) = \ln ( x - 2 ) + 5 ; \quad g ( x ) = \ln x$$

Accepted Answer

A)  Translate 2 units to the left and 5 units up. 
B)  Translate 5 units to the left and 2 units down. 
C)  Translate 2 units to the right and 5 units down. 
D)  Translate 2 units to the right and 5 units up. 
A)  Translate 2 units to the left and 5 units up. 
B)  Translate 5 units to the left and 2 units down. 
C)  Translate 2 units to the right and 5 units down. 
D)  Translate 2 units to the right and 5 units up.

Question 5

Match the function f with its graph.
-$$f ( x ) = \log _ { 5 } ( x - 1 )$$

Accepted Answer

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

Question 6

Use the product, quotient, and power rules of logarithms to rewrite the expression as a single logarithm. Assume that all
variables represent positive real numbers.
-$$\frac { 1 } { 2 } \log _ { a } x + 3 \log _ { a } y - 2 \log _ { a } x$$

Accepted Answer

A)  $\log _ { a } x ^ { 2 } y ^ { 3 }$ 
B)  $\log _ { a } x ^ { 4 } y ^ { 3 }$ 
C)  $\log _ { a } \sqrt { x } y ^ { 3 }$ 
D)  $\log _ { a } \left( \frac { y ^ { 3 } } { x ^ { 3 / 2 } } \right)$ 
A)  $\log _ { a } x ^ { 2 } y ^ { 3 }$ 
B)  $\log _ { a } x ^ { 4 } y ^ { 3 }$ 
C)  $\log _ { a } \sqrt { x } y ^ { 3 }$ 
D)  $\log _ { a } \left( \frac { y ^ { 3 } } { x ^ { 3 / 2 } } \right)$

Question 7

Solve the problem.
-Find the future value accumulated in an annuity after investing periodic payments of $134 for 8 years at an annual interest rate of 5%, with payments made and credited 4 times per year.

Accepted Answer

A)  $3139.66 
B)  $6279.31 
C)  $9418.97 
D)  $5232.76 
A)  $3139.66 
B)  $6279.31 
C)  $9418.97 
D)  $5232.76

Question 8

Determine the function which corresponds to the given graph.
- 
The asymptote is $x = - 2$.

Accepted Answer

A)  $y = \ln ( x - 2 )$ 
B)  $y = \ln x + 2$ 
C)  $y = \ln ( x + 2 )$ 
D)  $y = \ln x - 2$ 
A)  $y = \ln ( x - 2 )$ 
B)  $y = \ln x + 2$ 
C)  $y = \ln ( x + 2 )$ 
D)  $y = \ln x - 2$

Question 9

Solve the problem.
-Suppose you contribute to a fund that earns 5.5% annual interest. What should your quarterly payment be if you want to accumulate $190,000 in 18 years?

Accepted Answer

A)  $1873.72 
B)  $12,491.45 
C)  $1561.43 
D)  $2342.15 
A)  $1873.72 
B)  $12,491.45 
C)  $1561.43 
D)  $2342.15

Question 10

Match the function f with its graph.
-$$f ( x ) = \log _ { 5 } ( - x )$$

Accepted Answer

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

Question 11

Solve the problem.
-Find the present value of a loan with an annual interest rate of 5.9% and periodic payments of $778.63 for a term of 7 years, with payments made and interest charged 12 times per year.

Accepted Answer

A)  $96,254.83 
B)  $53,474.90 
C)  $42,779.92 
D)  $106,949.81 
A)  $96,254.83 
B)  $53,474.90 
C)  $42,779.92 
D)  $106,949.81

Question 12

Provide an appropriate response.
-The function $f ( x ) = 200 \frac { ( 1 + 0.06 / 4 ) ^ { x } - 1 } { 0.06 / 4 }$ describes the future value of a certain annuity. What is the annual interest rate?

Accepted Answer

The answer of Provide an appropriate response.
-The function \(f (...

Question 13

Find the domain of the function.
-$$f ( x ) = \log _ { 4 } \left( 100 - x ^ { 2 } \right)$$

Accepted Answer

A)  $[ - 10,10 ]$ 
B)  $( - 100,100 )$ 
C)  $( - 10,10 )$ 
D)  $( - \infty , - 10 ) \cup ( 10 , \infty )$ 
A)  $[ - 10,10 ]$ 
B)  $( - 100,100 )$ 
C)  $( - 10,10 )$ 
D)  $( - \infty , - 10 ) \cup ( 10 , \infty )$

Question 14

Solve the equation.
-$\log ( 3 + x ) - \log ( x - 2 ) = \log 2$

Accepted Answer

A)  $- 7$ 
B)  $\frac { 1 } { 2 }$ 
C)  7 
D)  $\varnothing$ 
A)  $- 7$ 
B)  $\frac { 1 } { 2 }$ 
C)  7 
D)  $\varnothing$

Question 15

Find the amount accumulated after investing a principal P for t years at an interest rate r.
-P = $1,000, t = 4, r = 4%, compounded semiannually (k = 2)

Accepted Answer

A)  $1148.69 
B)  $1169.86 
C)  $171.66 
D)  $1171.66 
A)  $1148.69 
B)  $1169.86 
C)  $171.66 
D)  $1171.66

Question 16

Find the exponential function that satisfies the given conditions.
-Initial population $= 1013$, doubling every 6 hours

Accepted Answer

A)  $\mathrm { P } ( \mathrm { t } ) = 6 \cdot 2 ^ { \mathrm { t } }$ 
B)  $P ( t ) = 1013 \cdot 2 ^ { t / 6 }$ 
C)  $P ( t ) = 1013 \cdot \left( \frac { 1 } { 2 } \right) ^ { t / 6 }$ 
D)  $P ( t ) = 1013 \cdot 2 ^ { 6 t }$ 
A)  $\mathrm { P } ( \mathrm { t } ) = 6 \cdot 2 ^ { \mathrm { t } }$ 
B)  $P ( t ) = 1013 \cdot 2 ^ { t / 6 }$ 
C)  $P ( t ) = 1013 \cdot \left( \frac { 1 } { 2 } \right) ^ { t / 6 }$ 
D)  $P ( t ) = 1013 \cdot 2 ^ { 6 t }$

Question 17

Determine the function which corresponds to the given graph.
- 
The asymptote is $x = - 3$

Accepted Answer

A)  $y = \log ( 3 - x )$ 
B)  $y = - \log ( x - 3 )$ 
C)  $y = - \log ( x + 3 )$ 
D)  $y = \log ( x + 3 )$ 
A)  $y = \log ( 3 - x )$ 
B)  $y = - \log ( x - 3 )$ 
C)  $y = - \log ( x + 3 )$ 
D)  $y = \log ( x + 3 )$

Question 18

Determine the doubling time of the investment.
-4.72% APR compounded monthly

Accepted Answer

A)  22.07 years 
B)  11.77 years 
C)  14.71 years 
D)  29.43 years 
A)  22.07 years 
B)  11.77 years 
C)  14.71 years 
D)  29.43 years

Question 19

Solve the inequality graphically.
-$$\left( \frac { 1 } { 9 } \right) ^ { - x } > \left( \frac { 1 } { 5 } \right) ^ { - x }$$

Accepted Answer

A) $x > 1$ B) $x > 0$ C) $x < 1$ D) $x < 0$ A) $x > 1$ B) $x > 0$ C) $x < 1$ D) $x < 0$

Question 20

Find the exact solution to the equation.
-$$\log x = - 3$$

Accepted Answer

A)  $x = 30$ 
B)  $x = - 30$ 
C)  $x = \frac { 1 } { 310 }$ 
D)  $x = \frac { 1 } { 1000 }$ 
A)  $x = 30$ 
B)  $x = - 30$ 
C)  $x = \frac { 1 } { 310 }$ 
D)  $x = \frac { 1 } { 1000 }$

Evaluate the logarithm. - $\log 100,000$

Use the product, quotient, and power rules of logarithms to rewrite the expression as a single logarithm. Assume that all variables represent positive real numbers. - $\log _ { 2 } 12 - \log _ { 2 } y$

Describe how to transform the graph of the basic function g(x) into the graph of the given function f(x). - $f ( x ) = \ln ( x - 2 ) + 5 ; \quad g ( x ) = \ln x$

Match the function f with its graph. - $f ( x ) = \log _ { 5 } ( x - 1 )$

Use the product, quotient, and power rules of logarithms to rewrite the expression as a single logarithm. Assume that all variables represent positive real numbers. - $\frac { 1 } { 2 } \log _ { a } x + 3 \log _ { a } y - 2 \log _ { a } x$

Solve the problem. -Find the future value accumulated in an annuity after investing periodic payments of $134 for 8 years at an annual interest rate of 5%, with payments made and credited 4 times per year.

Determine the function which corresponds to the given graph. - The asymptote is $x = - 2$ .

Solve the problem. -Suppose you contribute to a fund that earns 5.5% annual interest. What should your quarterly payment be if you want to accumulate $190,000 in 18 years?

Match the function f with its graph. - $f ( x ) = \log _ { 5 } ( - x )$

Solve the problem. -Find the present value of a loan with an annual interest rate of 5.9% and periodic payments of $778.63 for a term of 7 years, with payments made and interest charged 12 times per year.

Provide an appropriate response. -The function $f ( x ) = 200 \frac { ( 1 + 0.06 / 4 ) ^ { x } - 1 } { 0.06 / 4 }$ describes the future value of a certain annuity. What is the annual interest rate?

Find the domain of the function. - $f ( x ) = \log _ { 4 } \left( 100 - x ^ { 2 } \right)$

Solve the equation. - $\log ( 3 + x ) - \log ( x - 2 ) = \log 2$

Find the amount accumulated after investing a principal P for t years at an interest rate r. -P = $1,000, t = 4, r = 4%, compounded semiannually (k = 2)

Find the exponential function that satisfies the given conditions. -Initial population $= 1013$ , doubling every 6 hours

Determine the function which corresponds to the given graph. - The asymptote is $x = - 3$

Determine the doubling time of the investment. -4.72% APR compounded monthly

Solve the inequality graphically. - $\left( \frac { 1 } { 9 } \right) ^ { - x } > \left( \frac { 1 } { 5 } \right) ^ { - x }$

Find the exact solution to the equation. - $\log x = - 3$

Functions and Graphs

Polynomial, Power, and Rational Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Exam 3: Exponential, Logistic, and Logarithmic Functions

Evaluate the logarithm. - log⁡100,000\log 100,000log100,000

Use the product, quotient, and power rules of logarithms to rewrite the expression as a single logarithm. Assume that all variables represent positive real numbers. - log⁡212−log⁡2y\log _ { 2 } 12 - \log _ { 2 } ylog2​12−log2​y

Graph the function. Describe its position relative to the graph of the indicated basic function. - f(x)=1−6−x; relative to f(x)=6xf ( x ) = 1 - 6 ^ { - x } ; \text { relative to } f ( x ) = 6 ^ { x }f(x)=1−6−x; relative to f(x)=6x

Describe how to transform the graph of the basic function g(x) into the graph of the given function f(x). - f(x)=ln⁡(x−2)+5;g(x)=ln⁡xf ( x ) = \ln ( x - 2 ) + 5 ; \quad g ( x ) = \ln xf(x)=ln(x−2)+5;g(x)=lnx

Match the function f with its graph. - f(x)=log⁡5(x−1)f ( x ) = \log _ { 5 } ( x - 1 )f(x)=log5​(x−1)