6 Exponential Functions (Theory)

Graph of Exponential Functions When a > 1

Graph climbs

Graph of Exponential Functions When 0 > a > 1

Graph falls

Parts of the Exponential Function

Key Points of Exponential Functions

(0, 1) and (1, a)

If a is greater than 1, the horizontal asymptote is at…

y = 0

Domain of Exponential Functions

(−∞, ∞)

Range of Exponential Functions

(0, ∞), very close to 0 but not touching it, doesn’t include zero

Euler Number

2.71

How to Graph Exponential Functions

(1) Key points
- graph key points in relation to the function itself

(2) Shifts
- horizontal shift
- vertical shift
- negatives up front (change outputs of key points)
- constants up front (change outputs of key points)

(3) T-Table
- use t-table to find true values

3 Methods to Solving Exponential Equations

(1) Common Bases

(2) Logarithms

(3) Taking the n^th Root of Both Sides

Solving Exponential Equations with Common Bases

Same bases equal the same exponents

Inverse Property of Exponents

x

Taking the n^th Root of Both Sides

± when n is even, none when n is odd