Question

How do you graph `y = 3^x` by plotting points?

Answer 1

Simply calculate the `y` values for a range of `x` values and connect the dots.

Explanation:

I usually start with integer values, some positive, and some negative. Let's go with:
`x = -3`
`x = -2`
`x = -1`
`x = 0`
`x = 1`
`x = 2`
`x = 3`

The corresponding `y` values will be:
`y = 1/27`
`y = 1/9`
`y = 1/3`
`y = 1`
`y = 9`
`y = 27`

So we can see that the graph is quickly approaching zero in the negative region (really we could have seen this simply by observing that `3^x` is simply an increasingly large number in the denominator for negative `x`). In the positives, it is quickly increasing. The final result should be a graph looking like this:

graph{3^x [-5, 5, -2.5, 2.5]}