Question

Sketch the graph of f(x)=3^x and describe the end behavior of the graph?

Answer 1

`x rarr oo, y rarr oo` (As `x` approaches infinity, `y` approaches infinity)

Explanation:

Let's start by making a simple table of values

Remember, an exponential function has a default horizontal asymptote of `y=0`, as is visible below

Since the only transformation is a vertical compression of `3`, this will be simple to solve:

`f(-3)=3^(-3):` `y=1/27`
`f(-2)=3^(-2):` `y=1/9`
`f(-1)=3^(-1):` `y=1/3`
`f(0)=3^(0):` `y=1`
`f(1)=3^(1):` `y=3`
`f(2)=3^(2):` `y=9`
`f(3)=3^(3):` `y=27`

Remember that when you have an exponent of a negative value `(b^-a)`, `b` becomes the denominator put over `1`, and is put to the positive power of `a`.

The end behavior could be described that:

`x rarr oo, y rarr oo` (As `x` approaches infinity, `y` approaches infinity)