Use the graph shown to find the following. (a) The domain...

Use the graph shown to find the following. (a) The domain and range of the function (b) The intercepts, if any (c) Horizontal asymptotes, if any (d) Vertical asymptotes, if any (e) Oblique asymptotes, if any (a) What is the domain? Select the correct choice below and fill in any answer boxes within your choice. A. The domain of the function is {x | }. (Type an inequality. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as B. The domain of the function in the graph is the set of all real numbers.

Transcript

00:01 All right.

00:02 We need to use the graph shown to find the following.

00:05 We have to find the domain and range of the function, the intercepts, horizontal asymptotes, vertical asymptotes, or oblique asymptotes given there are any of these.

00:14 So let's start with finding the domain.

00:17 So domain has to do with the x values.

00:22 And if we look, those red lines represent our graph.

00:26 And it looks like they're pretty much covering all of our x values on the left and on the right, except where we have a vertical asymptotes.

00:33 And we have this vertical asymptote going straight up and down right here at x equals zero.

00:40 So when we have those vertical asymptotes, that's because we have a domain restriction there, meaning x cannot be zero at any time.

00:50 Okay? and so to write this as an inequality, we can write it as the set of x such that x does not equal zero.

01:10 Right? part b wants us to find, oh sorry, we still need to find the range.

01:17 So that's the domain.

01:17 Let's talk about the range.

01:21 The range is the y.

01:22 So that's basically going up and down on our graph.

01:24 So if we look at the span of that red graph, it looks like it's going all the way down and it's going to continue all the way down to negative infinity.

01:32 And then if we look at what it's doing when it's going up, well, it's just continuing in both the positive and negative direction on that range.

01:40 So our range is from negative infinity to infinity.

01:48 But if we need to put that as an interval, then we, as an inequality, we want to put it as y, such that y exist in the reels.

02:03 What that means is y can take on any value between negative infinity or infinity.

02:11 Let's talk about the intercepts.

02:14 So the intercepts occur when you're crossing or touching the x axis or crossing the y.

02:21 Axis.

02:23 So the only time we are crossing or touching the x -axis is at this point right here and at this point right here.

02:29 And notice that red line is never going to cross at the y -axis because we have an asymptote at x -equal zero there.

02:36 It cannot cross that vertical line, meaning it cannot cross the y -axis.

02:41 So there's no y intercepts, only x intercepts.

02:44 And those happen to fall at 2 -0 and negative to zero...

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