Question

I'd appreciate it if anyone could help ASAP! :) I'll give Brainliest!

Answer 1

We have been given a graph of function g(x) which is a transformation of the function $f(x)=3^x$

Now we have to find the equation of g(x)

Usually transformation involves shifting or stretching so we can use the graph to identify the transformation.

First you should check the graph of $f(x)=3^x$

You will notice that it is always above x-axis (equation is x=0). Because x-axis acts as horizontal asymptote.

Now the given graph has asymptote at x=-2

which is just 2 unit down from the original asymptote x=0

so that means we need shift f(x), 2 unit down hence we get:

$y=3^x$

but that will disturb the y-intercept (0,1)

if we multiply $3^x$ by 3 again then the y-intercept will remain (0,1)

Hence final equation for g(x) will be:

$g(x)=3(3^x)-2$