Consider the function shown in the following graph. The...

Consider the function shown in the following graph. The function is defined for all real numbers. Note: you can get an enlarged view of the graph by clicking on it. Use interval notation for both parts below. For what x values is the function increasing? For what x values is the function decreasing?

Transcript

00:01 All right, so we've been asked to find the values or the intervals for this function where it's increasing and decreasing.

00:06 And it's kind of a blurry graph, but to be quite honest, that doesn't really matter because all we really need to be able to do is read it from left to right.

00:14 So if i'm looking at this graph, i can see that i have the bottom of a hill here.

00:18 I have the top of a hill here, and i have the bottom of a hill here.

00:23 Now, this looks polynomial to me, so i'm going to also assume that that graph is going to keep going that direction and that direction.

00:30 Forever as it disappears off the graph.

00:33 Because if it's a polynomial function, all of the pertinent direction changes should be visible on the graph that they give us.

00:41 And this assumption that we're making is a valid assumption.

00:45 So what we do here is because we want to know the intervals from left to right where the graph is going up and down, we just need to know what these values are on the x -axis.

00:58 So notice that it's blurry.

01:01 I can't really tell how far up or down the graph goes.

01:04 I can only tell that it is going up and it is going down.

01:07 The numbers i need are going to come from the x -axis.

01:10 So if i take a look here in green, i'm going to make where my graph is going uphill green.

01:18 Think of it as like a roller coaster track, if you're familiar.

01:21 And then i'm going to make where my graph is going downhill yellow.

01:28 All right.

01:28 So it looks like i have two intervals of decrease.

01:31 So this is decreasing and this is decreasing...

Question

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