Question

Use transformations to graph the following function and submit the graph. Also state (a) the domain, (b) the range, (c) the horizontal asymptote.
f(x) = 3^(x+2) Use transformations to graph the following function and submit the graph. Also state (a) the domain, (b) the range, (c) the horizontal asymptote.
f(x) = 3^(x+2) @Mathematics

Answer 1

Uhm. By using transformations it says. So you have to find a known function which is similar to this one.

What pops out is :

\[e^x\]
We know the graph for this one. Then we find out the graph of..
\[e^{x+2}\]
Then adjust it a lil' bit to your function (They are very very similar, considering what is the value of "e") and you have it.

About the domain you have no problems since it's similar to the exponential, so it's defined in R.

The range. It never gets to negative values. As a matter of fact, even if x is negative you get 1 over something positive. Which is still positive. So the range is.

\[(0;+\infty)\]

About the horizontal asymptote, we could draw our conclusion pretty fast since we know it's similar to the exponential one, but anyhow:

\[\lim_{x->+\infty} 3^{x+2}\] Doesn't exist. While:


\[\lim_{x->-\infty} 3^{x+2}\] \[\frac{1}{3^\infty} = 0\]

So y = 0 is a left horizontal asymptote

Answer 2

ok- thank you.

Answer 3

So i dont understand what to put as my answer then

Answer 4

Plot:
http://www.wolframalpha.com/input/?i=plot+3^%28x%2B2%29
Domain:
\[x \in R\]
range:
\[(0;+\infty)\]
left horizontal asymptote:
y = 0

Answer 5

Thank you!!!