This document discusses exponential functions including: - Exponential growth graphs move away from the x-axis quickly when b > 1, while decay graphs move towards it when 0 < b < 1. Both have a y-intercept of (0, a). - Functions of the form y = a(b)x have a horizontal asymptote at y = 0. - The domain is the set of all input values x, while the range is the set of all output values y. - Examples are provided of identifying growth/decay, domain, range, asymptotes and y-intercepts of exponential functions. Graphing techniques including making tables and connecting points with smooth curves are also outlined.

1. 3.3 Graphs of
Exponential Functions

2. Exponential Growth Graphs
•When b > 1
▫ graph moves
away from x-axis
quickly from left to
right.
•y-intercept is at
point (0, a).

3. Exponential Decay Graphs
•When 0< b < 1
▫ graph moves
towards x-axis
quickly from left
to right.
•y-intercept is at
point (0, a).

4. Asymptotes
•An asymptote is a line that a graph
approaches (but does not touch) as it
moves away from the origin.
•Functions of the form
y = a(b)x have
horizontal asymptotes
at y = 0.

5. Domain & Range
•Domain & Range describe which
input/output values will work for a
given function.
•Domain – set of all input values (x’s)
▫ Look left and right
•Range – set of all output values (y’s)
▫ Look up and down
•Can be written using inequalities.

6. Example 1:
• Identify the following -
•Growth or Decay?
•Domain:
•Range:
•Asymptote:
•y-int:

7. Example 2:
• Identify the following -
•Growth or Decay?
•Domain:
•Range:
•Asymptote:
•y-int:

8. You Try!
• Identify the following -
•Growth or Decay?
•Domain:
•Range:
•Asymptote:
•y-int:

9. Graphing Exponential Functions
•To graph y = a(b)x
1. Make a table
2. Plot the points
3. Connect with a smooth curve
Be Careful:
• Don’t cross the asymptote (y = 0)!!
• Check that y-int is (0, a)!!

10. Example 1:
•Graph
• State the domain and range.

11. Example 2:
•Graph
• State the domain and range.

12. You Try!
•Graph
• State the domain and range.

13. Example 3:
•Graph
• State the domain and range.

14. Example 4:
•Graph
• State the domain and range.

15. You Try!
•Graph
• State the domain and range.

16. Transformations
•Remember:
•+ and – mean shift
•Changing the input shifts left/right
▫ Do the opposite!!
•Changing the output shifts up/down
•We will call the original function
y = a(b)x the “parent function”
• Its graph is the “parent graph”

17. Example 1:
• Identify the parent function and
describe the transformation on it.
1.
2.
3.

18. You Try!
• Identify the parent function and
describe the transformation on it.
1.
2.
3.

19. To Graph:
•Sketch the parent graph with a
dashed line.
• Shift points and draw final graph.
•Example:
•Graph
•Domain:
•Range:

20. Example 2:
•Graph
•Domain:
•Range:

21. You Try!
•Graph
•Domain:
•Range: