Question 1

Find functions f and g so that f $f \circ g = H$
-$$H ( x ) = \frac { 1 } { x ^ { 2 } - 5 }$$

Accepted Answer

A)  $f ( x ) = \frac { 1 } { x ^ { 2 } } ; \quad g ( x ) = - 1 / 5$ 
B)  $f ( x ) = \frac { 1 } { x } ; \quad g ( x ) = x ^ { 2 } - 5$ 
C)  $f ( x ) = x ^ { 2 } - 5 ; \quad g ( x ) = \frac { 1 } { x }$ 
D)  $f ( x ) = \frac { 1 } { x ^ { 2 } } ; \quad g ( x ) = x - 5$ 
A)  $f ( x ) = \frac { 1 } { x ^ { 2 } } ; \quad g ( x ) = - 1 / 5$ 
B)  $f ( x ) = \frac { 1 } { x } ; \quad g ( x ) = x ^ { 2 } - 5$ 
C)  $f ( x ) = x ^ { 2 } - 5 ; \quad g ( x ) = \frac { 1 } { x }$ 
D)  $f ( x ) = \frac { 1 } { x ^ { 2 } } ; \quad g ( x ) = x - 5$

Question 2

Graph the function.
-$$\mathrm { f } ( \mathrm { x } ) = \left( \frac { 1 } { 3 } \right) ^ { \mathrm { x } }$$
 
 A)

Accepted Answer

B)

C) 
  
D) 
  
B)

C) 
  
D)

Question 3

Use the horizontal line test to determine whether the function is one-to-one.
-

Accepted Answer

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

Question 4

Solve the problem.
-The population P of a predator mammal depends upon the number x of a smaller animal that is its primary food source. The population s of the smaller animal depends upon the amount a of a certain plant that is its
Primary food source. If $$P ( x ) = 3 x ^ { 2 } + 2$$ and s(a) = 2a + 5, what is the relationship between the predator mammal
And the plant food source? A) $\mathrm { P } ( \mathrm { s } ( \mathrm { a } ) ) = 4 \mathrm { a } ^ { 2 } + 20 \mathrm { a } + 27$

Accepted Answer

B)  $\mathrm { P } ( \mathrm { s } ( \mathrm { a } ) ) = 6 \mathrm { a } + 7$ 
C)  $P ( s ( a ) ) = 12 a ^ { 2 } + 30 a + 77$ 
D)  $\mathrm { P } ( \mathrm { s } ( \mathrm { a } ) ) = 12 \mathrm { a } ^ { 2 } + 60 \mathrm { a } + 77$ 
B)  $\mathrm { P } ( \mathrm { s } ( \mathrm { a } ) ) = 6 \mathrm { a } + 7$ 
C)  $P ( s ( a ) ) = 12 a ^ { 2 } + 30 a + 77$ 
D)  $\mathrm { P } ( \mathrm { s } ( \mathrm { a } ) ) = 12 \mathrm { a } ^ { 2 } + 60 \mathrm { a } + 77$

Question 5

Solve the problem.
-The formula D $$\mathrm { D } = 8 \mathrm { e } ^ { - 0.04 h }$$ can be used to find the number of milligrams D of a certain drug in a patient's bloodstream h hours after the drug has been given. When the number of milligrams reaches 4, the drug is to be
Given again. What is the time between injections?

Accepted Answer

A)  34.66 hrs 
B)  17.33 hrs 
C)  51.99 hrs 
D)  20.47 hrs 
A)  34.66 hrs 
B)  17.33 hrs 
C)  51.99 hrs 
D)  20.47 hrs

Question 6

Solve the problem.
-John Forgetsalot deposited $100 at a 3% annual interest rate in a savings account fifty years ago, and then he
promptly forgot he had done it. Recently, he was cleaning out his home office and discovered the forgotten
bank book. How much money is in the account?

Accepted Answer

The answer of Solve the problem.
-John Forgetsalot deposited $100 at...

Question 7

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator.
-$2 \ln \mathrm { e } ^ { 4.2 }$

Accepted Answer

A)  $2.1$ 
B)  $e ^ { 8.4 }$ 
C)  $8.4$ 
D)  $4.2$ 
A)  $2.1$ 
B)  $e ^ { 8.4 }$ 
C)  $8.4$ 
D)  $4.2$

Question 8

Choose the one alternative that best completes the statement or answers the question.
Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the
solution.
-$e ^ { x + 4 } = 7$

Accepted Answer

A)  {2.56} 
B)  {-2.86} 
C)  {-2.44} 
D)  {-2.92} 
A)  {2.56} 
B)  {-2.86} 
C)  {-2.44} 
D)  {-2.92}

Question 9

For the given functions f and g, find the requested composite function value.
-$$f ( t ) = \sqrt { t 4 + 18 t ^ { 2 } + 81 } , \quad g ( t ) = \frac { t + 3 } { 3 } ; \quad \text { Find } ( f \circ g ) ( 9 )$$

Accepted Answer

A)  25 
B)  360 
C)  31 
D)  625 
A)  25 
B)  360 
C)  31 
D)  625

Question 10

The graph of a one-to-one function f is given. Draw the graph of the inverse function f-1 as a dashed line or curve.
-$$f ( x ) = \frac { 4 } { x }$$
 
 A) Function is its own inverse

Accepted Answer

B) 
  
B)

Question 11

Solve the problem.
-A biologist has a bacteria sample. She records the amount of bacteria every week for 8 weeks and finds that the
exponential function of best fit to the data i $\mathrm { A } = 150 \cdot 1.79 \mathrm { t }$ . Express the function of best fit in the form $A = A_{ 0}e ^ { k t }$

Accepted Answer

The answer of Solve the problem.
-A biologist has a bacteria...

Question 12

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to two decimal places.
-$\log _ { 3 } 25$

Accepted Answer

A)  0.34 
B)  2.93 
C)  1.10 
D)  3.22 
A)  0.34 
B)  2.93 
C)  1.10 
D)  3.22

Question 13

The function f is one-to-one. Find its inverse.
-$$f ( x ) = \frac { 4 } { 7 x - 5 }$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \frac { 4 + 5 x } { 7 x }$ 
B)  $f ^ { - 1 } ( x ) = \frac { - 5 x - 4 } { 7 x }$ 
C)  $f ^ { - 1 } ( x ) = \frac { 7 x - 5 } { 4 }$ 
D)  $\mathrm { f } ^ { - 1 } ( x ) = \frac { 4 + 5 y } { 7 y }$ 
A)  $f ^ { - 1 } ( x ) = \frac { 4 + 5 x } { 7 x }$ 
B)  $f ^ { - 1 } ( x ) = \frac { - 5 x - 4 } { 7 x }$ 
C)  $f ^ { - 1 } ( x ) = \frac { 7 x - 5 } { 4 }$ 
D)  $\mathrm { f } ^ { - 1 } ( x ) = \frac { 4 + 5 y } { 7 y }$

Question 14

For the given functions f and g, find the requested composite function value.
-$f ( x ) = \frac { x - 6 } { x } , g ( x ) = x ^ { 2 } + 9 ; \quad$ Find $( g \circ f ) ( - 2 )$

Accepted Answer

A)  $\frac { 7 } { 13 }$ 
B)  13 
C)  $\frac { 145 } { 16 }$ 
D)  25 
A)  $\frac { 7 } { 13 }$ 
B)  13 
C)  $\frac { 145 } { 16 }$ 
D)  25

Question 15

Decide whether the composite functions, f $$f \circ g$$ nd $\mathbf { g } \circ \mathrm { f }$ f, are equal to x.
-$f ( x ) = 2 x , \quad g ( x ) = \frac { x } { 2 }$

Accepted Answer

A)  No, no 
B)  No, yes 
C)  Yes, no 
D)  Yes, yes 
A)  No, no 
B)  No, yes 
C)  Yes, no 
D)  Yes, yes

Question 16

Find the value of the expression.
-Let $\log _ { \mathrm { b } } \mathrm { A } = 2.087$ and $\log _ { \mathrm { b } } \mathrm { B } = 0.188$. Find $\log _ { \mathrm { b } } \mathrm { AB }$.

Accepted Answer

A)  $0.392$ 
B)  $11.101$ 
C)  $1.899$ 
D)  $2.275$ 
A)  $0.392$ 
B)  $11.101$ 
C)  $1.899$ 
D)  $2.275$

Question 17

Solve the problem.
-The size P of a small herbivore population at time t (in years) obeys the function $\mathrm { P } ( \mathrm { t } ) = 800 \mathrm { e } ^ { 0.24 \mathrm { t } }$ if they have enough food and the predator population stays constant. After how many years will the population reach 1,600?

Accepted Answer

A)  8.66 yrs 
B)  27.85 yrs 
C)  7.05 yrs 
D)  2.89 yrs 
A)  8.66 yrs 
B)  27.85 yrs 
C)  7.05 yrs 
D)  2.89 yrs

Question 18

Use transformations to graph the function.
-$$\text { Use the graph of } \log _ { 4 } x \text { to obtain the graph of } f ( x ) = - \frac { 1 } { 3 } \log _ { 4 } x \text {. }$$
 
 A)

Accepted Answer

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

Question 19

Decide whether or not the functions are inverses of each other.
-$$f ( x ) = \frac { 1 } { x + 6 } , g ( x ) = \frac { 6 x + 1 } { x }$$

Accepted Answer

A)  Yes 
B)  Yes; Exclude the value $\{ - 6 \}$ 
C)  No 
A)  Yes 
B)  Yes; Exclude the value $\{ - 6 \}$ 
C)  No

Question 20

Solve the equation. Express irrational answers in exact form and as a decimal rounded to 3 decimal places.
-$$\left( \frac { 1 } { 2 } \right) ^ { x } = 7 ^ { 1 - x }$$

Accepted Answer

A)  $\frac { \ln \left( \frac { 1 } { 2 } \right) + \ln 7 } { \ln 7 } \approx 0.644$
В) $\frac { \ln 7 } { \ln \left( \frac { 1 } { 2 } \right) + \ln 7 } \approx 1.553$ 
C)  $\ln \left( \frac { 1 } { 2 } \right) - \ln 7 \approx - 2.639$ 
D)  $\frac { \ln 14 } { \ln 28 } \approx 0.792$ 
A)  $\frac { \ln \left( \frac { 1 } { 2 } \right) + \ln 7 } { \ln 7 } \approx 0.644$
В) $\frac { \ln 7 } { \ln \left( \frac { 1 } { 2 } \right) + \ln 7 } \approx 1.553$ 
C)  $\ln \left( \frac { 1 } { 2 } \right) - \ln 7 \approx - 2.639$ 
D)  $\frac { \ln 14 } { \ln 28 } \approx 0.792$

Find functions f and g so that f $f \circ g = H$ - $H ( x ) = \frac { 1 } { x ^ { 2 } - 5 }$

Use the horizontal line test to determine whether the function is one-to-one. -

Solve the problem. -John Forgetsalot deposited $100 at a 3% annual interest rate in a savings account fifty years ago, and then he promptly forgot he had done it. Recently, he was cleaning out his home office and discovered the forgotten bank book. How much money is in the account?

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. - $2 \ln \mathrm { e } ^ { 4.2 }$

Choose the one alternative that best completes the statement or answers the question. Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - $e ^ { x + 4 } = 7$

For the given functions f and g, find the requested composite function value. - $f ( t ) = \sqrt { t 4 + 18 t ^ { 2 } + 81 } , \quad g ( t ) = \frac { t + 3 } { 3 } ; \quad \text { Find } ( f \circ g ) ( 9 )$

Solve the problem. -A biologist has a bacteria sample. She records the amount of bacteria every week for 8 weeks and finds that the exponential function of best fit to the data i $\mathrm { A } = 150 \cdot 1.79 \mathrm { t }$ . Express the function of best fit in the form $A = A_{ 0}e ^ { k t }$

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to two decimal places. - $\log _ { 3 } 25$

The function f is one-to-one. Find its inverse. - $f ( x ) = \frac { 4 } { 7 x - 5 }$

For the given functions f and g, find the requested composite function value. - $f ( x ) = \frac { x - 6 } { x } , g ( x ) = x ^ { 2 } + 9 ; \quad$ Find $( g \circ f ) ( - 2 )$

Decide whether the composite functions, f $f \circ g$ nd $\mathbf { g } \circ \mathrm { f }$ f, are equal to x. - $f ( x ) = 2 x , \quad g ( x ) = \frac { x } { 2 }$

Find the value of the expression. -Let $\log _ { \mathrm { b } } \mathrm { A } = 2.087$ and $\log _ { \mathrm { b } } \mathrm { B } = 0.188$ . Find $\log _ { \mathrm { b } } \mathrm { AB }$ .

Decide whether or not the functions are inverses of each other. - $f ( x ) = \frac { 1 } { x + 6 } , g ( x ) = \frac { 6 x + 1 } { x }$

Solve the equation. Express irrational answers in exact form and as a decimal rounded to 3 decimal places. - $\left( \frac { 1 } { 2 } \right) ^ { x } = 7 ^ { 1 - x }$

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

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Exam 4: Exponential and Logarithmic Functions

Find functions f and g so that f f∘g=Hf \circ g = Hf∘g=H - H(x)=1x2−5H ( x ) = \frac { 1 } { x ^ { 2 } - 5 }H(x)=x2−51​

Graph the function. - f(x)=(13)x\mathrm { f } ( \mathrm { x } ) = \left( \frac { 1 } { 3 } \right) ^ { \mathrm { x } }f(x)=(31​)x A) B) C) D)