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Mistake Master · AP Precalculus · Unit 2 · Step-Through Animation

One Shape, Two Directions

You'll learnto read the anatomy of an exponential function a·b^x.

An exponential function has one of the most disciplined shapes in mathematics: always climbing or always falling, never turning, never touching the line y = 0. Meet the anatomy of a · bx, watch the base swing the curve from decay to growth, and zoom into the tail that gets close to zero forever without arriving.

8 STEPS · 6 QUICK CHECKS · f(x) = a · bx · a > 0, b > 0, b ≠ 1 · v2

f(x) = a · b^x
Before you start
What you're looking at
The pattern 3, 6, 12, 24 building toward a smooth exponential curve with its horizontal asymptote.
The question
What operation makes each output from the one before, and what does the curve do to the line y = 0?
Watch for
The starting value a, the repeated factor b, and the tail that nears zero forever without touching.
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