The document discusses exponential functions of the form f(x) = a^x where a is a constant. It provides examples of exponential functions with a = 2 and a = 1/2. It describes the domain, range, and common point of exponential functions. The document also discusses transformations of exponential functions by adding or subtracting constants, and provides examples of sketching and describing transformed exponential functions. Finally, it lists common exponential expressions.

1. Exponential Functions
Exercise #19
Pre-Calculus 40S
f ( x) a x where a 0
Example
Sketch f ( x) 2x
y
x
Example
x
1
f ( x)
2
y
x

2. Exponential Functions
Exercise #19
Pre-Calculus 40S
Example
f ( x) 1x
y
x
Characteristics of Exponential Functions (in the above three examples)
A) Domain
B) Range
C) Common Point
If a 1 , then ____________________________________________
If 0 a 1 , then _________________________________________
If a 1 , then ___________________________________________

3. Exponential Functions
Exercise #19
Pre-Calculus 40S
Transformations
Determine what each of the following does to transform the graph y a x . State the
domain, range, y-intercept and whether the function is increasing or decreasing.
x
1. y 2 Transformation:
Domain: Range: Y Int: :
2. y 2x Transformation:
Domain: Range: Y Int: :
3. y 2x 1
Transformation:
Domain: Range: Y Int: :
4. y 2x 1 Transformation:
Domain: Range: Y Int: :
5. y 2x 1 Transformation:
Domain: Range: Y Int: :
Try
Sketch f ( x) 3x 3
4 hint: start with the function f ( x) 3x
y
x

4. Exponential Functions
Exercise #19
Pre-Calculus 40S
Try
2x
f ( x) 2
y
x
Try
f ( x) 3(2 x 1 )
y
x

5. Exponential Functions
Exercise #19
Pre-Calculus 40S
Common Exponents
21
22
23 31
24 32 41
25 33 42
26 34 43
27 35 44
28 36
29
210
51 61
52 62
53 63
54 64