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Problem 46 Hard Difficulty

Sketch the graph of the function.

$ f(x) = | x + 2 | $

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Video Transcript

we want to sketch the graph of this function. And so we should first think about its parent function. Y equals the absolute value. Becks. Hopefully, we have a feel for what that looks like. That's going to be that V shaped graph, which has a vertex at 00 and one line has a slope of one. The other has a slope of negative one. So then our function f of X is going to be that function but translated to the left to, and we can also find some points to plot. The pivotal point will be where the where we're taking the absolute value of zero, and so that will be negative, too. If you have X equals negative to the Y, value will be zero. Now let's find the coordinates of a couple points to the left of and to the right of that. So to the left of that, we could do negative three and negative four f of negative three is one f of negative four is, too. To the right of that, we could do negative one and zero f of negative. One is one N f of zero is, too. So let's go ahead and plot those points. So if negative to zero negative 31 negative four to negative 11 and zero to and then we can connect those. And we have that V shaped absolute value graph.