Free Printable Unit 3 Test Review

1.

Which equation matches the graph?

a)

y = 2^x+3

b)

y = 2^x + 3

c)

y = 2^x

d)

y = 2^-x

2.

What is the y-intercept of the function?

a)

2

b)

3

c)

1

d)

-2

3.

What type of function is f(x)=2(1/7)^x ?

a)

Exponential Growth

b)

Linear

c)

Exponential Decay

d)

None of the Abovee

4.

What type of function is y = 7(5/4)^x?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None of the above

5.

Is the pictured graph growth, decay, or linear or none?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None

6.

What is the equation of the horizontal asymptote for following exponential function?

a)

y = -4

b)

y > -4

c)

y < -4

d)

(0, -3)

7.

solve for x.

$2^x=2^{3x-4}$

a)

2

b)

-2

c)

1/2

d)

4/3

8.

solve for x.

$11^4=11^{-x}$

a)

-4

b)

4

c)

1/4

d)

-1/4

9.

Solve 8 = 2^5x+7

a)

x = ⅘

b)

x = ¼

c)

x = -⅘

d)

x = -¼

10.

What is the asymptote of y = 2^x - 3

a)

y = 0

b)

y = -3

c)

x = 0

d)

x = -3

11.

Marburn has 80 total students in our High School. It is projected to grow at rate of 2% every year. How many students will be in the High School in 5 years from now?

a)

72.3 students

b)

88.3 students

c)

199.1 students

d)

80 students

12.

The population of a town is decreasing at a rate of 5% per year. This year there are 10,000 people in this town, how many people will be left in 20 years from now? (round to the nearest whole number)

a)

26,533 people

b)

358 people

c)

1 person

d)

3,585 people

13.

Find the balance in the account after the given period.

$5000 deposit earning 1.5% compounded quarterly after 3 years

a)

$5,229.70

b)

$7,604.38

c)

$7,777.27

d)

$5,538.86

14.

An investment of $9,875 earns 4.8% interest compounded monthly over 12 years. Approximately how much INTEREST is earned on the investment?

a)

$7,457.95

b)

$10,359.57

c)

$17,546.55

d)

$484.57

15.

If $1,000 is invested at 16% interest, compounded continuously, for five years, what is the ending balance?

a)

$1,225,54

b)

$2,225.54

c)

$22,255.40

d)

$225.54

16.

Rewrite log₂8 = 3 in exponential form/

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

17.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

18.

Write the exponential equation as a logarithm
$6^3=216$

a)

$\log_6\left(3\right)=\ 216$

b)

$\log_6\left(216\right)=3$

c)

$\log_3\left(6\right)=216$

d)

$\log_{216}\left(6\right)=3$

19.

Evaluate log₄1

a)

1

b)

0

c)

4

d)

undefined

20.

Evaluate
$\log_5\ 125$

a)

2

b)

5

c)

3

d)

No Solution

21.

Use the change of base formula and your calculator to approximate the log.

a)

A

b)

B

c)

C

d)

D

22.

$\log_2\ 18$

Using the change of base rule, what is this logarithm equivalent to?

a)

4.965

b)

4.17

c)

3.408

d)

2.212

23.

Converting forms: Convert the given logarithmic equation into its exponential form. $\log_x25=3$

a)

$x^3=25$

b)

$3^x=25$

c)

$25^3=x$

d)

$25^x=3$

24.

Condensing Logs: Use properties of logarithms to condense the given problem to a single log with no coefficient.

a)

A

b)

B

c)

C

d)

D

25.

Condensing Logs: Use properties of logarithms to condense the given problem to a single log with no coefficient.

a)

A

b)

B

c)

C

d)

D

26.

Condensing Logs: Use properties of logarithms to condense the given problem to a single log with no coefficient.

$2\log_6a+\log_6b-3\log c$

a)

$\log_6\left(\frac{a^2}{bc^3}\right)\$

b)

$\log_6\left(\frac{\left(ab\right)^2}{c^3}\right)\ \$

c)

$\log_6\left(\frac{a^2b}{c^3}\right)$

d)

$\log_6\left(\frac{ab}{c}\right)^{\frac{2}{3}}\$

27.

Expanding Logs: Use properties of logarithms to expand the given problem completely and choose the correct answer.

$\log(xy^2)$

a)

$\log x+2\log y$

b)

$\log x+\log y^2$

c)

$\log x-2\log y$

d)

$\log x+\log y+\log2$

28.

Solving Exponential Equations Using Logarithms:

Solve for x

$6^x=80$

a)

4.3820

b)

2.4457

c)

5.0321

d)

1.9031

29.

Solving Exponential Equations Using Logarithms:

Solve for x

$4^x-5=12$

a)

0.489

b)

2.552

c)

0.893

d)

2.044

30.

Solving Exponential Equations Using Logarithms:

Solve for x

$8e^{x+1}=40$

a)

0.61

b)

2.6

c)

No Solution

d)

-1.61

31.

Solving Log Equations: Use Properties of logarithms to solve the given equation for the variable and choose the correct solution.

a)

A

b)

B

c)

C

d)

D

32.

Solving Log Equations: Use Properties of logarithms to solve the given equation for the variable and choose the correct solution.

a)

5

b)

13

c)

84

d)

-20

33.

Solve: $\log\left(6x-4\right)=\log\left(2x+24\right)$

a)

x = 10

b)

x = 7

c)

x = 5

d)

x = 6

34.

Solve: $\log_2\left(x+4\right)=\log_2\left(3x-6\right)$

a)

x = 2

b)

x = 6

c)

x = 4

d)

x = 5

35.

Solve: $\log12=\log\left(x+2\right)+\log3$

a)

x = 2

b)

x = 3

c)

x = 6

d)

x = 12

36.

Solve: $\log_418=\log_43+\log_4\left(x-8\right)$

a)

x = 2

b)

x = -2

c)

x = 14

d)

x = 9

37.

f(x)=log₅(x+4) - 2

Describe the asymptote

a)

Horizontal Asymptote x = -4

b)

Vertical Asymptote x = -4

c)

Horizontal Asymptote x = 4

d)

Vertical Asymptote x = 4

38.

f(x)=log₅(x+4) - 2

Find the Domain and Range

a)

Domain: x ≥ -4

Range: all real numbers

b)

Domain: all real numbers

Range: y ≥ -4

c)

Domain: all real numbers

Range: y > -4

d)

Domain: x > -4

Range: all real numbers

39.

f(x)=log₅(x+4) - 2

Describe the transformation

a)

translation 4 units to the right, 2 units down

b)

translation 4 units to the left, 2 units down

c)

translation 4 units to the up, 2 units right

d)

translation 4 units to the up, 2 units left

40.

Which graph matches the function

*remember the transformation has shifted it right 3 and down 3

a)

b)

c)

d)

Unit 3 Test Review

Total questions: 40

Worksheet time: 4hrs 17mins

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