Hi, I have a math question that I need help with:

g:-> 3(1.3)^x

State equations for any asymptotes to the graph of g.

I know what an asymptote is, but I do not understand this question...so lost. Help would be greatly appreciated.

Thanks so much

I'm a little unsure what your notation means. You have
g:-> 3(1.3)^x
I'm supposing this means g(x)=3(1.3)^x
I should point out that the term asymptote is one of those math terms with a variety of meanings. For this problem there are no vertical asymptotes, but look at what happens when x goes to - infinity: g(x) approaches 0. Thus the x-axis would be considered a horizontal asymptote for g(x). The x-axis equation, BTW, is y = 0.

To find the equation for any asymptotes to the graph of the function g(x) = 3(1.3)^x, we need to determine if there are any horizontal or vertical lines that the graph approaches or gets arbitrarily close to.

First, let's consider vertical asymptotes. Vertical asymptotes occur when the function approaches infinity or negative infinity as x approaches a certain value. In this case, since the function g(x) does not involve any division by x, there are no vertical asymptotes.

Next, let's consider horizontal asymptotes. Horizontal asymptotes occur when the function approaches a specific value as x approaches infinity or negative infinity. To find horizontal asymptotes, we need to look at the behavior of the function as x approaches these limits.

As x approaches negative infinity, the base of the exponential function, 1.3^x, becomes smaller and smaller, approaching zero. This means that g(x) approaches 3 multiplied by zero, which is 0. Therefore, the x-axis y = 0 is a horizontal asymptote for g(x).

To summarize, the equation for the asymptotes of the graph of g(x) = 3(1.3)^x is:
- There are no vertical asymptotes.
- The x-axis y = 0 is a horizontal asymptote.