Graphing Exponential Functions
Example
Graph
![](./articles_imgs/151/algebr15.gif)
Solution
Step 1 Make a table of ordered pairs.
We will let x be integers from -3 through 3.
![](./articles_imgs/151/algebr32.gif)
Note:
Recall this useful property of
negative exponents:
![](./articles_imgs/151/algebr19.gif)
Thus,
![](./articles_imgs/151/algebr22.gif)
Step 2 Plot the ordered pairs.
See the graph.
![](./articles_imgs/151/algebr29.gif)
Step 3 Sketch a smooth curve through the plotted points.
The smooth curve represents all the ordered pairs that satisfy
The x-axis acts as a horizontal asymptote for
This is because
as the values of x approach positive infinity, +∞, the values of
approach 0, but never reach 0.
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