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Graphs of Exponential Functions

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State

The graph of f(x) = bˣ passes through (0, 1), has domain all reals and range (0, ∞), and hugs the horizontal asymptote y = 0 on its shrinking side.

Show

2ˣ runs through (−1, 1/2), (0, 1), (1, 2); far left, 2⁻¹⁰ ≈ 0.001 — near the floor, never on it.

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