Question 1

Use a calculator to find an approximate solution to the equation.
-$$\mathrm { e } ^ { - \mathrm { t } } = 0.02$$

Accepted Answer

A)  $3.712$ 
B)  $- 3.912$ 
C)  $4.012$ 
D)  $3.912$ 
A)  $3.712$ 
B)  $- 3.912$ 
C)  $4.012$ 
D)  $3.912$

Question 2

Choose the graph which matches the function.
-$f(x)=e^{3 x}-2$

Accepted Answer

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

Question 3

Simplify the expression.
-$$e ^ { \ln 6 }$$

Accepted Answer

A)  $\frac { 1 } { 6 }$ 
B)  $e ^ { 6 }$ 
C)  6 
D)  $\ln 6$ 
A)  $\frac { 1 } { 6 }$ 
B)  $e ^ { 6 }$ 
C)  6 
D)  $\ln 6$

Question 4

Find the amount accumulated after investing a principal P for t years at an interest rate r.
-P = $480, t = 6, r = 10%, compounded quarterly (k = 4)

Accepted Answer

A)  $847.01 
B)  $850.35 
C)  $388.19 
D)  $868.19 
A)  $847.01 
B)  $850.35 
C)  $388.19 
D)  $868.19

Question 5

Compute the exact value of the function for the given x-value without using a calculator.
-$$f ( x ) = 3 \cdot 25 ^ { x } \text { for } x = - 3 / 2$$

Accepted Answer

A)  45 
B)  375 
C)  $\frac { 3 } { 125 }$ 
D)  $- \frac { 3 } { 125 }$ 
A)  45 
B)  375 
C)  $\frac { 3 } { 125 }$ 
D)  $- \frac { 3 } { 125 }$

Question 6

Match the function f with its graph.
-$$f ( x ) = \log _ { 1 / 3 } ( x )$$

Accepted Answer

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

Question 7

Solve the inequality graphically.
-$4 ^ { - x } > 7 ^ { - x }$

Accepted Answer

A)  $x > 1$ 
B)  $x  0$ 
A)  $x > 1$ 
B)  $x  0$

Question 8

Graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, symmetry,
boundedness, extrema, asymptotes, and end behavior.
-f(x) = ln (3 - x)

Accepted Answer

@#IMG-DLM&
The domain is @#LAT-DLM&, and the range is all re

Question 9

Solve the equation.
-$$2 ( 10 - 2 x ) = 64$$

Accepted Answer

A)  5 
B)  2 
C)  32 
D)  $- 2$ 
A)  5 
B)  2 
C)  32 
D)  $- 2$

Question 10

Graph the function. Describe its position relative to the graph of the indicated basic function.
-$$f ( x ) = 4 ^ { x - 2 } ; \text { relative to } f ( x ) = 4 ^ { x }$$

Accepted Answer

A)  Moved left 2 unit(s)
  
B)  Moved up 2 unit(s)
  
C)  Moved right 2 unit(s)
  
D)  Moved down 2 unit(s)
  
A)  Moved left 2 unit(s)
  
B)  Moved up 2 unit(s)
  
C)  Moved right 2 unit(s)
  
D)  Moved down 2 unit(s)

Question 11

Decide if the function is an exponential function. If it is, state the initial value and the base.
-$$y = x ^ { 4.7 }$$

Accepted Answer

A)  Exponential Function; base $= 4.7$; initial value $= 0$ 
B)  Exponential Function; base $= x$; initial value $= 1$ 
C)  Exponential Function; base $= x$; initial value $= 0$ 
D)  Not an exponential function 
A)  Exponential Function; base $= 4.7$; initial value $= 0$ 
B)  Exponential Function; base $= x$; initial value $= 1$ 
C)  Exponential Function; base $= x$; initial value $= 0$ 
D)  Not an exponential function

Question 12

Find the logistic function that satisfies the given conditions.
-

Accepted Answer

A)  $f ( x ) = 3 \cdot 0.8 ^ { x }$ 
B)  $f ( x ) = 4.32 \cdot 1.2 ^ { x }$ 
C)  $f ( x ) = 3 \cdot 1.2 ^ { x }$ 
D)  $f ( x ) = 3 \cdot 1.4 ^ { x }$ 
A)  $f ( x ) = 3 \cdot 0.8 ^ { x }$ 
B)  $f ( x ) = 4.32 \cdot 1.2 ^ { x }$ 
C)  $f ( x ) = 3 \cdot 1.2 ^ { x }$ 
D)  $f ( x ) = 3 \cdot 1.4 ^ { x }$

Question 13

Find the domain of the function.
-$$f ( x ) = \ln \left( ( x + 3 ) ^ { 2 } \right)$$

Accepted Answer

A)  $( - \infty , 3 ) \cup ( 3 , \infty )$ 
B)  $( - 3 , \infty )$ 
C)  $( - \infty , - 3 ) \cup ( - 3 , \infty )$ 
D)  $( - \infty , \infty )$ 
A)  $( - \infty , 3 ) \cup ( 3 , \infty )$ 
B)  $( - 3 , \infty )$ 
C)  $( - \infty , - 3 ) \cup ( - 3 , \infty )$ 
D)  $( - \infty , \infty )$

Question 14

Decide if the function is an exponential function. If it is, state the initial value and the base.
-$$y = x ^ { 7 x }$$

Accepted Answer

A)  Exponential Function; base $= 7 \mathrm { x }$; initial value $= 0$ 
B)  Exponential Function; base $= x$; initial value $= 1$ 
C)  Not an exponential function 
D)  Exponential Function; base $= x$; initial value $= 0$ 
A)  Exponential Function; base $= 7 \mathrm { x }$; initial value $= 0$ 
B)  Exponential Function; base $= x$; initial value $= 1$ 
C)  Not an exponential function 
D)  Exponential Function; base $= x$; initial value $= 0$

Question 15

Find the domain of the function.
-$$f ( x ) = 4 \ln | x - 3 |$$

Accepted Answer

A)  $( - \infty , 12 ) \cup ( 12 , \infty )$ 
B)  $( - \infty , - 3 ) \cup ( - 3 , \infty )$ 
C)  $( - \infty , 3 ) \cup ( 3 , \infty )$ 
D)  $( 3 , \infty )$ 
A)  $( - \infty , 12 ) \cup ( 12 , \infty )$ 
B)  $( - \infty , - 3 ) \cup ( - 3 , \infty )$ 
C)  $( - \infty , 3 ) \cup ( 3 , \infty )$ 
D)  $( 3 , \infty )$

Question 16

Solve the problem.
-The relationship between intensity I of light (in lumens) at a depth of $x$ feet in Lake $X$ is given by $\log \frac { \mathrm { I } } { 12 } = - 0.00264 x$. What is the intensity at a depth of 50 feet?(Round to the nearest ten-thousandth.)

Accepted Answer

A)  $11.6408$ lumens 
B)  $0.0615$ lumens 
C)  $0.7379$ lumens 
D)  $8.8549$ lumens 
A)  $11.6408$ lumens 
B)  $0.0615$ lumens 
C)  $0.7379$ lumens 
D)  $8.8549$ lumens

Question 17

Find the exact solution to the equation.
-$6 \ln ( x - 5 ) = 1$

Accepted Answer

A)  $x = e ^ { 6 } + 5$ 
B)  $x = e ^ { 1 / 6 + 5 }$ 
C)  $x = 6 e + 5$ 
D)  $x = e ^ { 1 / 6 } - 5$ 
A)  $x = e ^ { 6 } + 5$ 
B)  $x = e ^ { 1 / 6 + 5 }$ 
C)  $x = 6 e + 5$ 
D)  $x = e ^ { 1 / 6 } - 5$

Question 18

Describe how to transform the graph of g(x) = ln x into the graph of the given function. Graph the function.
-$f(x)=\log _{4} x$

Accepted Answer

A)  Reflect across the line $y = x$ and vertically shrink by a factor $\frac { 1 } { \ln 4 }$ 
  
B)  Reflect across the $y$-axis and shift right 4 units
  
C)  Reflect across the $x$-axis and Vertically shrink by a factor of $\frac { 1 } { \ln 4 }$ 
  
D)  vertically shrink by a factor $\frac { 1 } { \ln 4 }$
  
A)  Reflect across the line $y = x$ and vertically shrink by a factor $\frac { 1 } { \ln 4 }$ 
  
B)  Reflect across the $y$-axis and shift right 4 units
  
C)  Reflect across the $x$-axis and Vertically shrink by a factor of $\frac { 1 } { \ln 4 }$ 
  
D)  vertically shrink by a factor $\frac { 1 } { \ln 4 }$

Question 19

Match the function f with its graph.
-$$f ( x ) = \log 3 x$$

Accepted Answer

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

Question 20

Evaluate the logarithm.
-$\log _ { 8 } ( 32 )$

Accepted Answer

A)  $\frac { 5 } { 3 }$ 
B)  $\frac { 5 } { 4 }$ 
C)  $\frac { 4 } { 3 }$ 
D)  $\frac { 3 } { 2 }$ 
A)  $\frac { 5 } { 3 }$ 
B)  $\frac { 5 } { 4 }$ 
C)  $\frac { 4 } { 3 }$ 
D)  $\frac { 3 } { 2 }$

Use a calculator to find an approximate solution to the equation. - $\mathrm { e } ^ { - \mathrm { t } } = 0.02$

Choose the graph which matches the function. - $f(x)=e^{3 x}-2$ $Choose the graph which matches the function. - f(x)=e^{3 x}-2$

Simplify the expression. - $e ^ { \ln 6 }$

Find the amount accumulated after investing a principal P for t years at an interest rate r. -P = $480, t = 6, r = 10%, compounded quarterly (k = 4)

Compute the exact value of the function for the given x-value without using a calculator. - $f ( x ) = 3 \cdot 25 ^ { x } \text { for } x = - 3 / 2$

Match the function f with its graph. - $f ( x ) = \log _ { 1 / 3 } ( x )$

Solve the inequality graphically. - $4 ^ { - x } > 7 ^ { - x }$

Graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. -f(x) = ln (3 - x)

Solve the equation. - $2 ( 10 - 2 x ) = 64$

Decide if the function is an exponential function. If it is, state the initial value and the base. - $y = x ^ { 4.7 }$

Find the logistic function that satisfies the given conditions. -

Find the domain of the function. - $f ( x ) = \ln \left( ( x + 3 ) ^ { 2 } \right)$

Decide if the function is an exponential function. If it is, state the initial value and the base. - $y = x ^ { 7 x }$

Find the domain of the function. - $f ( x ) = 4 \ln | x - 3 |$

Solve the problem. -The relationship between intensity I of light (in lumens) at a depth of $x$ feet in Lake $X$ is given by $\log \frac { \mathrm { I } } { 12 } = - 0.00264 x$ . What is the intensity at a depth of 50 feet?(Round to the nearest ten-thousandth.)

Find the exact solution to the equation. - $6 \ln ( x - 5 ) = 1$

Describe how to transform the graph of g(x) = ln x into the graph of the given function. Graph the function. - $f(x)=\log _{4} x$ $Describe how to transform the graph of g(x) = ln x into the graph of the given function. Graph the function. - f(x)=\log _{4} x$

Match the function f with its graph. - $f ( x ) = \log 3 x$

Evaluate the logarithm. - $\log _ { 8 } ( 32 )$

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

Use a calculator to find an approximate solution to the equation. - e−t=0.02\mathrm { e } ^ { - \mathrm { t } } = 0.02e−t=0.02

Choose the graph which matches the function. - f(x)=e3x−2f(x)=e^{3 x}-2f(x)=e3x−2

Simplify the expression. - eln⁡6e ^ { \ln 6 }eln6

Find the amount accumulated after investing a principal P for t years at an interest rate r. -P = $480, t = 6, r = 10%, compounded quarterly (k = 4)

Compute the exact value of the function for the given x-value without using a calculator. - f(x)=3⋅25x for x=−3/2f ( x ) = 3 \cdot 25 ^ { x } \text { for } x = - 3 / 2f(x)=3⋅25x for x=−3/2

Match the function f with its graph. - f(x)=log⁡1/3(x)f ( x ) = \log _ { 1 / 3 } ( x )f(x)=log1/3​(x)

Solve the inequality graphically. - 4−x>7−x4 ^ { - x } > 7 ^ { - x }4−x>7−x

Graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. -f(x) = ln (3 - x)

Solve the equation. - 2(10−2x)=642 ( 10 - 2 x ) = 642(10−2x)=64

Graph the function. Describe its position relative to the graph of the indicated basic function. - f(x)=4x−2; relative to f(x)=4xf ( x ) = 4 ^ { x - 2 } ; \text { relative to } f ( x ) = 4 ^ { x }f(x)=4x−2; relative to f(x)=4x

Decide if the function is an exponential function. If it is, state the initial value and the base. - y=x4.7y = x ^ { 4.7 }y=x4.7

Find the logistic function that satisfies the given conditions. -

Find the domain of the function. - f(x)=ln⁡((x+3)2)f ( x ) = \ln \left( ( x + 3 ) ^ { 2 } \right)f(x)=ln((x+3)2)

Decide if the function is an exponential function. If it is, state the initial value and the base. - y=x7xy = x ^ { 7 x }y=x7x

Find the domain of the function. - f(x)=4ln⁡∣x−3∣f ( x ) = 4 \ln | x - 3 |f(x)=4ln∣x−3∣

Find the exact solution to the equation. - 6ln⁡(x−5)=16 \ln ( x - 5 ) = 16ln(x−5)=1

Describe how to transform the graph of g(x) = ln x into the graph of the given function. Graph the function. - f(x)=log⁡4xf(x)=\log _{4} xf(x)=log4​x

Match the function f with its graph. - f(x)=log⁡3xf ( x ) = \log 3 xf(x)=log3x

Evaluate the logarithm. - log⁡8(32)\log _ { 8 } ( 32 )log8​(32)

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

Use a calculator to find an approximate solution to the equation. - $\mathrm { e } ^ { - \mathrm { t } } = 0.02$

Choose the graph which matches the function. - $f(x)=e^{3 x}-2$ $Choose the graph which matches the function. - f(x)=e^{3 x}-2$

Simplify the expression. - $e ^ { \ln 6 }$

Compute the exact value of the function for the given x-value without using a calculator. - $f ( x ) = 3 \cdot 25 ^ { x } \text { for } x = - 3 / 2$

Match the function f with its graph. - $f ( x ) = \log _ { 1 / 3 } ( x )$

Solve the inequality graphically. - $4 ^ { - x } > 7 ^ { - x }$

Solve the equation. - $2 ( 10 - 2 x ) = 64$

Decide if the function is an exponential function. If it is, state the initial value and the base. - $y = x ^ { 4.7 }$

Find the domain of the function. - $f ( x ) = \ln \left( ( x + 3 ) ^ { 2 } \right)$

Decide if the function is an exponential function. If it is, state the initial value and the base. - $y = x ^ { 7 x }$

Find the domain of the function. - $f ( x ) = 4 \ln | x - 3 |$

Find the exact solution to the equation. - $6 \ln ( x - 5 ) = 1$

Describe how to transform the graph of g(x) = ln x into the graph of the given function. Graph the function. - $f(x)=\log _{4} x$ $Describe how to transform the graph of g(x) = ln x into the graph of the given function. Graph the function. - f(x)=\log _{4} x$

Match the function f with its graph. - $f ( x ) = \log 3 x$

Evaluate the logarithm. - $\log _ { 8 } ( 32 )$