Free Printable Chapter 3 Review! :)

Worksheets

Chapter 3 Review! :)

Total questions: 52

Worksheet time: 4hrs 44mins

Name

Class

Date

A collectible car has been going up in price by 10% each year. If the car is already worth $29,000, how much will the car be worth in 5 years?

$0.29

$2,900,000,000

$46,704.79

$145,000

The expression 12(1.015)^t models the population of elephants in a wildlife refuge after t years since 1975.
Is the population of elephants increasing or decreasing?

Increasing

Decreasing

The expression 12(1.015)^t models the population of elephants in a wildlife refuge after t years since 1975.
What does the value 12 represent?

The predicted increase in number of elephants in the refuge each year.

The predicted decrease in number of elephants in the refuge each year.

The number of years it will take for the elephant population to stop increasing.

The initial amount of elephants in the park.

What is the equation that best represents the graph?

y=2^y

y=2^x

y=2^-x

y=x²

What is the domain and range of the function y=2^x?

Use the graph to help!

Domain: −∞<x<∞

Range: y>0

Domain: −∞<x<∞

Range: y>1

Domain: −2<x<∞

Range: y>0

Domain: −∞<x<∞

Range: y<0

Given y=3^xdetermine the y-intercept

(0,1)

(0,3)

No Y-intercept

y=1

What is the horizontal asymptote for the graph of

f(x)=13(0.5)^x?

y=0.5

y=13

y=6

y=0

For $f\left(x\right)=3^x$ , find the correct graph, asymptote, domain and range.

For $f\left(x\right)=\left(\frac{1}{2}\right)^x$ , find the correct graph, asymptote, domain and range.

10.

Given the function $y=3\left(2\right)^x$ , fill in the blank in the table when $x=5$ .

7776

$-30$

11.

Rewrite log₂8 = 3 in exponential form.

2⁸ = 3

2³ = 8

3² = 8

8³ = 2

12.

Rewrite 3⁴ = 81 in logarithmic form.

log₃4 = 81

log₈₁3 = 4

log₃81 = 4

log₄81 = 3

13.

log₅25 = ?

125

14.

Evaluate:
log₄16

1/2

-2

15.

Solve for x.
3^x = 27

16.

Logarithmic functions are the inverse of...

Linear Functions

Exponential Functions

Quadratic Functions

Polynomial Functions

17.

Select all the transformations that apply.

y = -2 log _1/2x

Vertical stretch by 2

Vertical shrink by 1/2

Reflection across the y-axis

Reflection across the x-axis

18.

Which equation is the inverse of the equation above?

19.

Write log_b(xy) as two logs

log_bx+log_by

log_bx-log_by

log_bx*log_by

log_bx/log_by

20.

Write log_b(x/y) as two logs

log_bx-log_by

log_bx+log_by

log_bx*log_by

log_bx/log_by

21.

Evaluate log_b(b)

-1

22.

Log with a base "e" (log_e) is the same thing as...

"e"

Natural Logarithm (LN)

Common Logarithm (Log)

Natural Log, base "e"
LN_e

23.

Simplify e^ln(x)

24.

Simplify log₄4^3x

4^3x

25.

Rewrite 3⁴ = 81 in logarithmic form.

log₃4 = 81

log₈₁3 = 4

log₃81 = 4

log₄81 = 3

26.

Rewrite log_b(xⁿ)

nlog_bx

(log_bx)ⁿ

xⁿlog_bx

log_b(xⁿ)

27.

Write the expression as a single logarithm. Then simplify if possible.
log₅3 + log₅6 + log₅9

log₅69

log₅56

log₅162

log₅98

28.

Write the expression as a single logarithm. Then simplify if possible.
log 6 - log 3 + 2 log 7

log 98

log 78

log 56

log 45

29.

The common logarithm has what base?

-e

30.

Evaluate log₅20 to the third decimal place

0.537

2.996

1.301

1.861

31.

Expand

6log₈v-2log₈u

6log₈u-2log₈v

3log₈u-2log₈v

6log₈u+2log₈v

32.

Courtney saved up $2,200 working as a waitress over the summer. She put this money into a bank account that earned 5.2% interest and is compounded daily. How much will she have in her account at the end of 4 years?

$2201.25

$2694.55

$2707.45

$2708.63

33.

Use multiple log properties to write as a single log:
3log₂x - log₂y + log₂z

log₂(x/(yz))

log₂(x³yz)

log₂(x³z/y)

log₂(x³/(yz))

34.

Expand completely: log(2x⁵)

log 2 + 5log x

5log 2 + 5log x

5log 2 + log x

log 10 + log x

35.

Solve log(x) + log(x+3) = 1

-2

-5

36.

log₅(4x-7)=log₅(x+5)

37.

-20

38.

no solution

only 6

6 and -2

39.

x = 5 and x = -2

x = -2

x = 5

x = -10 and x = 10

40.

3^{2x – 6} = 81

x = log 4

x = 5

x = 4

x = -1

41.

7ⁿ⁺¹⁰- 8 = 6

-7.374

-8.643

-7.360

-8.853

42.

To solve, 16^5x = 64^x+7, what would be the correct set-up?

There is more than one correct answer.

4^4(5x)=4^16(x+7)

8^2(5x)=8^8(x+7)

4^2(5x)=4^3(x+7)

2^4(5x)=2^6(x+7)

43.

Solve for x:
5 e^6x+3= 0.1

-1.152

0.232

-3.077

-0.854

44.

4^(x-2)= 64^(x+1)

-2/5

-5/2

7/2

2/7

45.

How much money would need to be invested today if you want $40,000 in 18 years at 4.5% if compounded continuously.

$19,923.22

$17,794.32

$89,916.32

$1 Bob

46.

Solve for x.
e^2x-e^x-2 = 0

x = 0

x = ln 2, ln -1

x = ln 2, ln 0

x = ln2

47.

Find the time required for an investment of $1000 to grow to $5000 at an interest rate of 8% per year compounded monthly. (round to nearest year)

1 year

242 years

20 years

13 years

48.

f(x)=2^x-1-3

f(x)=2^x-1+3

f(x)=2^x+1-3

f(x)=2^x+1+3

49.

Given the original exponential function defined by y=4^x, how would the graph change if the function were:

y=2(4)^x-3+1?

Vertically stretched by a factor of 2, right 3, and up 1

Vertically compressed by a factor of 1/2, left 3 and down 1

Vertically compressed by a factor of 1/2, right 3, and down 1

Vertically stretched by a factor of 2, left 3, and up 1

50.

How has the function $7\left(3\right)^x-5$ been transformed from the parent function $7\left(3\right)^x$ ?

Shifted up 5

Shifted down 5

Reflection over the x-axis

Reflection over the y-axis

51.

How has the function $-5\left(3\right)^x$ been transformed from the parent function $5\left(3\right)^x$ ?

Shifted up 5

Shifted down 5

Reflection over the x-axis

Reflection over the y-axis

52.

How has the function $-5\left(3\right)^x+4$ been transformed from the parent function $5\left(3\right)^x$ ?

Shifted up 4

Shifted down 4

Shifted down 5

Reflection over the x-axis

Reflection over the y-axis

Reset

Chapter 3 Review! :)

Total questions: 52

Worksheet time: 4hrs 44mins

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