Exponential Functions

We want to draw a graph of the given exponential function. $f (x) = 2 (3)^{x}$ Because the $base$ of the function is greater than $1,$ we know that this is an exponential growth function. To draw the graph, we will start by making a table of values.

$x$	$2 (3)^{x}$	$y = 2 (3)^{x}$
$- 3$	$2 (3)^{- 3}$	$0.074 \dots$
$- 2$	$2 (3)^{- 2}$	$0.222 \dots$
$- 1$	$2 (3)^{- 1}$	$0.666 \dots$
$0$	$2 (3)^{0}$	$2$
$1$	$2 (3)^{1}$	$6$
$2$	$2 (3)^{2}$	$18$

The ordered pairs $(- 3, 0.074),$ $(- 2, 0.222),$ $(- 1, 0.666),$ $(0, 2),$ $(1, 6),$ and $(2, 18)$ all lie on the graph of the function. Now, we will plot and connect these points with a smooth curve.

Exponential Functions 1.7 - Solution