Exponential Functions

Vocabulary

100

What is the definition of a function?

A relation between a set of inputs having one output each.

200

What is the definition of an Asymptote?

A line that a graph gets closer to as the value of x increases or decreases without bound. 

300

What is the definition of an Exponential Function?

f(x) = ab^x, where a and b are real numbers with a is not equal or unequal to 0, b>0, and b is not equal or unequal to 0.

400

What is the definition of and exponential decay function?

a>0 and 0<b<1

500

What is the definition of an Exponential Growth Function?

a>0 and b>1

Quotient of Like Bases

100

Solve: 5⁶/5⁹

1/125

200

Solve: x^-9/x4

1/x⁵

300

Solve: 7⁴·7⁵/7⁹

1

400

Solve: 12⁴/3⁴

256

500

Solve: (3/4)⁵/ 3/4

81/256

Product of Like Bases

100

Solve: x³ · x^-7

1/x⁴

200

Solve: (2^-5)(2³)

1/4

300

Solve: (-2^-3)(-2^-2)

-1/32

400

Solve: (4^-2)(4^-3)

1/1024

500

Solve: 5⁶·5^-9

1/15,625

Negative Exponents

100

Solve: 2^-3

1/8

200

Solve: 5^-2

1/25

300

Solve: (-2)^-3

-1/8

400

Solve:(-3)^-4

-1/27

500

Solve: (-16)^-5

-1/1,048,576

Bonus

100

What is the solution if 9^0?

1

200

Explain whether the statement is True or False:

7⁰ = 7⁵/7⁵

True

300

Explain whether the statement is True or False:

8⁴/8⁴ = 8

False: The exponents are meant to be subtracted, leaving it to be 8⁰ = 1. 

400

Explain whether the statement is True or False:

(0.12)(0.12)(0.12) / (0.12)(0.12)(0.12) = 0.12

False. It would be 1. 

500

Explain whether the statement is True or False:

5⁶ x 1/25 = 5⁸

False. 5⁶ x 1/25 = 625

5⁸ = 390,625