section 6-1: introduction to exponential functions

Chapter 6:Exponential and

Logarithmic Functions

Section 6-1:Introduction to

Exponential Functions

Objective

Discover by point-wise plotting what the graph of an exponential function looks like.

Exponential Function

An exponential function is a function whose general equation is:

xy a b

Where a and b stand for constants, b is positive, and x and y are independent and dependent

variables, respectively.

Example:

Consider the function f(x) = 2x

Calculate f(4), f(3), f(2), and f(1).

Chapter 6:Exponential and

Logarithmic Functions

Section 6-2:Exponentiation for

Positive Integer Exponents

Objective

Use the definition of exponentiation to evaluate expressions that have powers with positive integer exponents, in preparation for learning the properties in the next section.

ExponentiationFor Positive Integer Exponents

xn means the product of n x’s.

Names in the Expression xn

x is called the base.

n is called the exponent.

The whole term xn is called a power.

Agreement

If the base of a power consists of more than one symbol, then it must be placed in parentheses. Fore example,

(xy)5

(x-y)5

(-x)5

Otherwise, the exponent only applies to one symbol. For example,

xy5 = x(y5)

Evaluate the Following Examples

4

4

5

1) 2 3

2) 2

3) 7

Given f(x) =3x

Evaluate:f (3)

f (2)

f (1)

Plot the graph of the function.

HOMEWORK:Complete Worksheet