Help sketching a graph from exponential function lesson

[Steph Annie]

Sketch the graph of f(x)=3x. Give the domain of f(x) in interval notation. Solve when f(x) = 1. Show your solution on the graph.

I did fine with the f(x) = 32 part I think. My sketch reflected the value of x increasing, and the value of y increasing. However y increased very rapidly as compared with x. My graph is an example of exponential growth....I think.

Here are my points. Could you check them and make your own graph of the same points to see if it looks correct?


f(x)=3^x

f(-2) = 3^-2
=1/3²
= 1/9

f(x)=3^x

f(-3) = 3^-3
=1/3³
=1/27

If x=-2 and x=-3

f(x) =3^x

My points chart.

x f(x)
-2 1/9 (-2, 1/9)
-3 1/27 (-3, 1/27)
-1 1/3 (-1, 1/3)
0 1 (0,1)
1 3 (1,3)
2 9 (2,9)
3 27 (3, 27)
4 81 (4,81)


I plotted x=-2 and x=-3 and then the points from my chart.

How's it looking so far? If all looks correct then the final is to solve when f(x) = 1. How would I do that?