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Problem 19 Easy Difficulty

Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations.

$ y = \sin (\frac{1}{2} x) $


$y=\sin (x / 2):$ Start with the graph of
$y=\sin x$ and stretch horizontally by a
factor of 2.

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Video Transcript

to graph this function, we're going to start by looking at the graph of the standard function y equals sign of X, so we know that it has a period of two pi. That's the with that one cycle, and we knew it goes up to a height of one and down to a height of negative one. So it looks roughly like this. Now what happens to it if we multiply the X by 1/2 that represents a horizontal stretch, so it's going to be two times as wide. So we say horizontal stretch by a factor of two that changes the period. The width of one cycle is now going to be four pi instead of two pi. So if you want to draw it out that far, we can still goes up to a height of one and down to a height of negative one. That didn't change. So now we have the graph that is stretched out wider, like so

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