Question

$e(x) = 1(3)^x$

Explanation:

Step1: Identify function form

This is an exponential function: $e(x) = 3^x$ (since $1(3)^x=3^x$)

Step2: Calculate key points

For $x=-2$: $e(-2)=3^{-2}=\frac{1}{9}\approx0.11$
For $x=-1$: $e(-1)=3^{-1}=\frac{1}{3}\approx0.33$
For $x=0$: $e(0)=3^{0}=1$
For $x=1$: $e(1)=3^{1}=3$
For $x=2$: $e(2)=3^{2}=9$ (note: 9 is above the grid's max y-value of 6)

Step3: Plot points and draw curve

Plot $(-2, 0.11)$, $(-1, 0.33)$, $(0,1)$, $(1,3)$; draw a smooth increasing curve that approaches the x-axis (y=0) as $x\to-\infty$, and rises steeply as $x$ increases.

Answer:

The graph of $e(x)=3^x$ is an increasing exponential curve passing through $(0,1)$, $(1,3)$, with points $(-1,\frac{1}{3})$, $(-2,\frac{1}{9})$, approaching the x-axis for negative $x$ and growing rapidly for positive $x$.