1. Pre-Calculus :Chapter 3.1 Exponential Functions and Their Graphs
Mrs.Volynskaya
Pre-Calculus :Chapter 3.1
Exponential Functions and
Their Graphs
The exponential function f with base a is denoted by
f(x) = ax
and x is any real number.

2. Graph y = 2x
x y -2 -1 1 2
2-2 =
2-1 = 1 2 4

3. y = 2-x
x y -2 -1 1 2 4 2 1

4. y = 2x + 1
x y -2 -1 1 2
5/4
3/2 2 3 5
Graph shifted up one.

5. y = 2x+1
x y -2 -1 1 2 1 2 4 8 -3
Graph shifted left one.

6. y = -2x
y = 2x
x y -2 -1 1 2
-1/4
-1/2 -1 -2 -4
Reflects about x-axis

7. The number e
e = …
y = ex
x y -2 -1 1 2
1/e2
1/e 1 e
e2 = 7.389

8. Using the One-to-One Property
Ex.

9. Formulas for Compound Interest
For n compoundings per year:
yearly 1
monthly 12
semi-ann 2
daily 365
For continuous compounding:

10. Ex. A total of $12,000 is invested at an annual
percentage rate of 9%. Find the balance
after 5 years if it is compounded
a. quarterly b. continuously
A = 12,000e.09(5)
A = $18,819.75
A = $18,726.11