g(x) = 1/5 (5)^(x+4)

For the given function g, which of the following equivalent forms shows the y-coordinate of the y-intercept of the graph of y=g(x) in the xy-plane as a constant or coefficient?

A. g(x) = 125(5)^x

B. g(x) = 25(5)^(x+1)

C. g(x) = 5(5)^(x+2)

D. g(x) = (5)^(x+3)

Choice A is correct, but why?

The key part of the question is “shows the -coordinate of the -intercept…** as a constant or coefficient.**” That means you’re looking for a certain number—in this case, the -intercept—to appear somewhere in the correct answer choice.

So let’s find the -intercept! Remember, the -intercept is where , so we can plug in 0 for and simplify.

So the -intercept is 125. Which answer choice has a 125 in it? Only choice A.