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Problem 38 Hard Difficulty

Sketch the graph of the piecewise defined function.
$f(x)=\left\{\begin{array}{ll}{2 x+3} & {\text { if } x<-1} \\ {3-x} & {\text { if } x \geq-1}\end{array}\right.$

Answer

see graph

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Video Transcript

Let's start by drawing our access. Okay. Now we have zero U minus one minus two. It's not that close. Yeah, minus two minus three. We have one 23 You have one to three. Minus one, minus two, minus three. Now to Bloods. F of X equals two X plus three. Let's give dropouts off a little table. Okay, lets try. Exit course minus minus one and exit course minus two. If X equals minus one, then we have two times minus one plus three. Right. So that's when it's two plus three. And that's one. Next if X equals minus two, get two times minus two. Plus three. Get minus four plus three. So minus one. Supporting those two points in, we'll need two points because this is just a straight line. So So first. So So first we have the point minus one and one. Okay, Next, we have minus one minus two and minus one over here. Okay, We can draw a line. All right, now, because X is strictly less than one. This so called here, it will be a hard Oh, circle. Okay. And we can also we move this point hit too. Oops. Yep. Now that's the first graph. Now for the 2nd 1 let's let's try F. Whoops. Let's try F of minus one again. Now, this is for F of XY course three minus X and if ever their exes minus one. When we get three minus minus one two. Minuses. Make a plus. So three plus one, that's four. Next, we have f of now, let's put zero if a zero so three minus zero is just three. Good. So let's put points. So we have minus one and four, which is appear. This is a solid liner because X can be equal to minus one. You have 03 Just this point here. Now we can draw straight line through that.