Graphing Exponential Functions — Cheat sheet

CHEAT SHEET · FREE

Three points and one line

Point	Why
$\left(-1, \dfrac{1}{a}\right)$	a negative power is a reciprocal
$(0, 1)$	$a^0 = 1$ , for every base
$(1, a)$	$a^1 = a$

Asymptote: the $x$ -axis, $y = 0$ . The curve approaches it and never meets it.

Base	Shape
$a > 1$	growth: rises left to right
$0 < a < 1$	decay: falls left to right

Domain: every real number. Range: $y > 0$ .

Change	Effect
$\left(\dfrac{1}{a}\right)^x = a^{-x}$	reflection in the $y$ -axis - decay is growth mirrored
$a^x + k$	every point lifts by $k$ , and the asymptote goes to $y = k$