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**Jhevon** for the second, the graph stretches four times its original length on any finite interval.

think of it this way. we use our x-value as a measure of the horizontal distance traveled, right? so when we say, for example, f(1), what we are saying is, "the value of the function when we are one horizontal unit from the y-axis"

now, staying with f(1), and assume we are dealing with a function f(x) on a finite inteval. let's say we want to get to f(1) from the function f(x). well, we just plug in x = 1 and we're done.

what about f(4x). well, to get f(1), we need to plug in x = 1/4, since f(4*(1/4)) = f(1). so you see, we reach the desired value, four times as fast. no longer do we have to go all the way to 1, we can just travel to 1/4, which is 4 times LESS the distance. so f(4x) shrinks the graph by **a factor** **of** 4. or we can equivalently say, it shrunk by 1/4, to say the graph is now 1/4 of its original length

what about f((1/4)x)? to get to f(1), we need to plug in x = 4, since f((1/4)*4) = f(1). so now instead of going to 1, we have to go all the way to 4 to get the same value. so the graph stretches 4 times as long as it was, and therefore, we stretch it by **a factor of** 4.