Pre-Calculus 12 Notes

By: Gen L.

Lesson 2: Graphing Exponential Functions

Graphing

Sketch out the following:

Generalizations

For , where is a constant:

• if , grows. ()
• if , decays. ()
• if , .
• As , the slope increases.
• There's technically one restriction: .
  • You get a lot of 'artifacts' if you don't stay above 0. Try it, you'll see why.

Properties of

• -int is always 1.
• There (technically) is no -intercept.
• Domain:
• Range:
• Asymptote: .

General Form of Exponentials

• : Vertical Stretch (reflects in -axis)
• : Horizontal Stretch (reflects in -axis)
• : Horizontal Shift
• : Vertical Shift

Mapping Notation

Graphing Tips

Sketch a graph of

• Note the transformations ().
• Note the basis graph ().
• Mark the asymptote (dotted line and labelled).

Now, try sketching a graph of .

• Note the transformations ().
• Note the basis graph ().
• Mark the asymptote (, dotted line and labelled).

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