The graph of a rational function f is shown below. Assume...

The graph of a rational function f is shown below. Assume that all asymptotes and intercepts are shown and that the graph has no "holes". Use the graph to complete the following. (a) Write the equations for all vertical and horizontal asymptotes. Enter the equations using the "and" button as necessary. Select "None" as necessary. Vertical asymptote(s): Horizontal asymptote(s): (b) Find the domain and range of f. Write each answer as an interval or union of intervals. Domain: Range: (c) Find all x-intercepts and y-intercepts. Check all that apply. x-intercept(s): -4, 4, -2, None y-intercept(s): -2, 2, 4, None

Transcript

00:01 The first thing that we want to do is figure out the vertical asymptotes, and that's pretty easy to find because everything's kind of drawn here on the graph.

00:09 So the dashed lines are the vertical and horizontal asymptotes.

00:12 Essentially, what it means is your function, which you have here in red, is getting really, really close to those lines, but it's never going to touch or cross them.

00:23 So that's really what an asymptote means.

00:25 So the one that's going up and down right here in blue, that is your vertical asymptote.

00:32 And just look to see the number that it's going through, which it appears to be a negative 4.

00:39 And since it's vertical, all vertical lines are of the form x equals a number.

00:45 So the vertical asymptote is x equals negative 4.

00:51 The horizontal asymptote is the horizontal dashed line that the function is getting really close.

00:57 Close to on both ends, but it's never going to touch it and it's never going to cross.

01:02 Horizontal asymptotes are always of the form y equals.

01:06 And it looks like it's going through two on the y -axis, so it's the line.

01:11 Y equals two.

01:15 Now it's time to find the domain and the range.

01:20 So domain is all of the x values.

01:23 You can see that we can have all the x values here for the domain, negative 4.

01:30 Again, the graph is never going to actually touch negative 4.

01:36 So the domain is everything before negative 4.

01:40 So i'm going to put negative infinity.

01:41 You can see that left part of the graph is going off to negative infinity here with that arrow.

01:49 And it's going to go up to negative 4, but it's not going to ever touch negative 4.

01:54 You're not going to ever have an x value of negative 4.

01:57 So that's why we have to put a parentheses.

02:01 And then we're going to do union to join it...

Question

Please give Ace some feedback