# Graphing Exponents and logs.

• May 14th 2013, 11:33 PM
Gurp925
Graphing Exponents and logs.
Hi, I had two question assigned to me, both of which stumped me if some one would help it would be great.

Sketch a graph of the following and then fill in the table below:

f(x)=3x
g(x)=(3^2x)-3
h(x)=g-1(x)

Now i cant sketch them but for f and g i sketch them by imputing values for x and graph but for H I don't know how to graph that? it seems like a inverse function of G(x) but i cant quiet wrap my head around it.

The table asks for each function state

1) domain - All real numbers
2)range - All real numbers
3)asymptotes- i wrote no asymptotes for any
4)y intercept - 1)x=0 2)x=0.5 3) didn't get this far
5)x intercept - didn't get this far

• May 15th 2013, 03:51 AM
Shakarri
Re: Graphing Exponents and logs.
You can rewrite h(x) so that it doesn't contain g. $h(x)= (3^{2x})-3-x$
When sketching h(x) it is similar to your graph of g(x) but just subtracting x, redraw your sketch of g(x) but subtracting larger values of x as you move long the real line.

The y intercept occurs at x=0, your intercept for g(x) is incorrect.
The x intercept occurs at y=0, the x intercept might not exist, you can tell from your sketches.
• May 15th 2013, 03:22 PM
Gurp925
Re: Graphing Exponents and logs.
My mistake, H(x) = (g^-1)(x) not g-1(x)
• May 15th 2013, 09:37 PM
Gurp925
Re: Graphing Exponents and logs.
Anyone? how do i do this is its ^ the above comment
• May 16th 2013, 07:27 AM
Shakarri
Re: Graphing Exponents and logs.
$g(x)=y=3^{2x}-3$

$y+3=3^{2x}$

$ln(y+3)=ln3^{2x}$

$ln(y+3)=2xln3$

$\frac{ln(y+3)}{2ln3}=x$

So then $g^{-1}(x)=\frac{ln(x+3)}{2ln3}$