5. f(x) = -4 / (x^2 - 3x) We are only looking at END...

5. f(x) = -4 / (x^2 - 3x) We are only looking at END Behaviors, so if you don't have enough information, look at the limits as x approaches positive and negative infinity to help sketch the graph. Hint: lim x->+inf f(x) = 0^- and lim x->-inf f(x) = 0^- There is a part of the graph we haven't learned to sketch yet, so don't worry about the middle section of the graph Key Points to Graph: Sketch Graph:

Transcript

00:01 Okay, so this question is asking us to graph f of x is equal to negative 4 over x squared minus 3x and the problem itself gives us some hints.

00:17 It tells us that we're looking for n behaviors and we should be thinking about the limits of the function as x approaches 0 from both the left and the right.

00:27 It's asking us to note any key points to graph and then just to roughly sketch the graphs.

00:33 And so in terms of key points here, we're going to want to find the asymptotes.

00:37 You can think of the asymptotes as the line as it approaches 0 as one or both of the y coordinates tends to infinity.

00:49 And so we're going to want to think of our vertical asymptotes and that's going to be the x asymptotes and our horizontal asymptotes.

00:56 Those are going to be our y asymptotes.

00:58 So there are these things called oblique asymptotes as well, but we don't have to worry about that with this one.

01:04 Okay, so we're going to go ahead and just draw our graph out and the center is 0.

01:13 And so here we want to think about key points.

01:17 So our key points here are going to be what or where the function approaches 0.

01:25 So one place the function approaches 0 is going to be at 0.

01:30 So one of the x asymptotes, right, so if we plugged in 0 at the bottom here it would tend towards 0.

01:35 So one of our asymptotes is going to be 0 and that's going to be our vertical asymptote.

01:40 So we'll go ahead and say x asymptotes are going to be equal to, so x asymptotes are going to be 0...

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