1. 55. Graphing Exponential Functions

2. Steps to draw a graph Draw the asymptote
In your calculator, make a table with the starting x value that makes the exponent = 0
Plot points
Connect with a smooth curve that approaches asymptote on one side and infinity or – infinity on the other

3. Graph y = x 2 +0 1.
Draw an asymptote 2.
Start table at x = 0

4. draw a curve that “hugs” the x-axis, and moves up to the right. 0, 1 2
EXAMPLE 2
Graph the function. x 1 y 2 1.
Draw the asymptote
Plot and (1, 2)
draw a curve that “hugs” the x-axis, and moves up to the right. 0, 1 2 2.

5. EXAMPLE 3 Graph the function. 5 y = – 2 Draw the asymptote 51 y -1
-5/2
y = – 5 2 x
Draw the asymptote
Plot (0, –1) and
Draw a curve that begins just below the x-axis, and moves down to the right.
1, – 5 2

6. EXAMPLE 4 Graph the function. x 1 Graph y = 2 +1 4 Draw the asymptote1 y 3
3/2
Graph y = 2 1 4 x +1
Draw the asymptote
Plot (0, 3) and
draw a curve that begins just above the x-axis and moves up to the left. 1, 3 2

7. -2 EXAMPLE 5 Graph y = –3 2 5 x Draw the asymptote 1, –3.21 y -5
-3.2 -2
Draw the asymptote
1, –3.2
Plot (0, –5) and
Draw a curve that begins just below the x-axis, and moves down to the left.

8. Example

9. Example

10. Review: Characteristics of Exponential Functions
Domain:
Range:
Asymptotes:
Zeros:
Intercepts:
Intervals of Increase and Decrease:
End Behaviors:
Transformations: