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 y-coordinate of the y-intercept…as a constant or coefficient.” That means you’re looking for a certain number—in this case, the y-intercept—to appear somewhere in the correct answer choice.

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

g(0)=\dfrac{1}{5}(5)^{0+4}\\\\g(0)=\dfrac{1}{5}(5)^4\\\\g(0)=5^{-1}\left(5^4\right)\\g(0)=5^3\\g(0)=125

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

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