1. Exponential Functions

2. Basic Definitions

3. Exponential Function
where a > 0 and a ≠ 1.
With translations:

4. Natural Exponential Function
where e is the natural base and e  2.718…

5. Try This (-∞, ∞) (-∞, ∞) (-∞, ∞) (0, ∞) (0, ∞) (0, ∞) Inc. Dec. Inc.
Function
f(x) = 2x
h(x) = (0.5)x
g(x) = ex
Domain
Range
Increasing or Decreasing
Point Shared On All Graphs
(-∞, ∞)
(-∞, ∞)
(-∞, ∞)
(0, ∞)
(0, ∞)
(0, ∞)
Inc.
Dec.
Inc.
(0, 1)

6. Properties of f (x) = ax
Domain: Range: Increasing for: Decreasing for: Point Shared On All Graphs: Asymptote:
(-∞, ∞)
(0, ∞)
a > 1
0 < a < 1
(0, 1)
y = 0

7. Graph Sketching
Use translation of functions to graph the following. Determine the domain and range of each.
f (x) = -5(x + 2) – 3
2. g(x) = (1 / 3)(x – 1) + 2

8. Try This Determine the values of x for which 2x > x 4.
Write your answer using interval notation. You may use your graphing calculator.

9. Try This
An isotope of sodium, 24Na, has a half-life of 15 hours. A sample of this isotope has mass 2 g.
Find the amount remaining after 60 hours.
Find the amount remaining after t hours.
Estimate the amount remaining after 4 days.
Use a graph to estimate the time required for the mass to be reduced to 0.01 g.