Question

How do you graph exponential function `f(x) = 3^x`?

Answer 1

see explanation.

Explanation:

to sketch f(x) = `3^x`

choose appropriate values for x and substitute them into the function to obtain corresponding value of y. Then plot these coordinate points on squared paper.

`f(0) = 3^0 =1`
`f(1) = 3^1 = 3`
`f(2) = 3^2 = 9`
`f(3) = 3^3 = 27`

Now you can plot the points (0 ,1 ) , (1 , 3 ) , (2 , 9 ) and (3 , 27 )

There are also negative values of x that can be considered.

Here make use of the fact that `color(red)(a^-m = 1/a^m)`

`f(- 1 ) = 3^-1 = 1/3^1 = 1/3`
`f(-2) = 3^-2 = 1/3^2 = 1/9`
`f(-3) = 3^-3 = 1/3^3 = 1/27`
Now you can plot the points`(- 1 , 1/3 ) , ( -2 , 1/9 ) and (-3 , 1/27)`

I have included the graph of `f(x) = 3^x`
graph{3^x [-10, 10, -5, 5]}