6.1 Day 1

1

January 27, 2020

Warm UpFill out each table of values. You may use a calculator.

x ­10 ­5 ­1 0 1 5 10

f(x)

1. f(x) = 4x

2. f(x) = (1/2)x

x ­10 ­5 ­1 0 1 5 10

f(x)

For each problem, as x increases, does f(x) increase or decrease?1:2:

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6.1 Day 1

2

January 27, 2020

6.1 - Exponential Growth and DecayDefinitions:

• exponential function:

b is a positive number other than 1a cannot equal 0

• If b > 1 : exponential _________

• If 0<b<1: exponential ________

• b is called the growth or decay factor.

• asymptote: a line that the graph approaches more and more closely without touching/crossing.

6.1 Day 1

3

January 27, 2020

Ex 1:

Parent?

Growth or Decay?

Transformations?

Asymptote?

x

y

x f(x)­10­5­101510

a: vertical stretch or shrink factor

­a: reflected over the x­axis

h: horizontal translation

k: vertical translation

y = k is the asymptote!!!

D:

R:

6.1 Day 1

4

January 27, 2020

Ex 2:

Base:

Exponent:

Growth or decay:

a: h: k:

Asymptote:

Transformations: