Question

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) Find all x-intercepts and y-intercepts. Check all that apply. x-intercept(s): -1, -2, -4, None y-intercept(s): -4, -2, -1, None (b) 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): (c) Find the domain and range of f. Write each answer as an interval or union of intervals. Domain: Range:

          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) Find all x-intercepts and y-intercepts. Check all that apply.
x-intercept(s): -1, -2, -4, None
y-intercept(s): -4, -2, -1, None
(b) 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):
(c) Find the domain and range of f.
Write each answer as an interval or union of intervals.
Domain:
Range:

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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) Find all x-intercepts and y-intercepts. Check all that apply.
x-intercept(s): -1, -2, -4, None
y-intercept(s): -4, -2, -1, None
(b) 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):
(c) Find the domain and range of f.
Write each answer as an interval or union of intervals.
Domain:
Range:

Added by Laura S.

Precalculus with Limits

Ron Larson 2nd Edition

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Solved by Expert Julie Silva

02/25/2022

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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) Find all x-intercepts and y-intercepts. Check all that apply. x-intercept(s): -1, -2, -4, None y-intercept(s): -4, -2, -1, None (b) 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): (c) Find the domain and range of f. Write each answer as an interval or union of intervals. Domain: Range:

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Transcript

00:01 So in this problem, we were given the graph of function.

00:02 As you can see, i put a sketch of it here on the left or on the right.

00:06 So the first thing i want to do in part a is identify the x as well as the y intercepts.

00:11 Remember, the x intercepts are going to occur when the graph hits your x axis.

00:16 So here's your x axis.

00:17 So where does it hit? well, the only place that this graph hits is when x is negative 1.

00:21 So the only x intercept in this case is negative 1.

00:25 Now, the y intercept tells us the point where the graph is going to hit our y axis.

00:29 So this would be our y.

00:30 Y -axis, and the only point our graph hits the y -axis is right here when y is negative 2.

00:35 So that would be your only y intercept.

00:38 All right.

00:38 Next, let's take a look at part b.

00:40 They want us to find the equation for both our vertical and horizontal asymptopes.

00:45 So the vertical asymptote is going to be that vertical line that's right here.

00:49 Well, at what x values does this occur? well, it occurs at negative 2, which means our vertical asymptope is the equation x equals negative 2.

00:57 Next, we want to write the equation for the horizontal asymptote.

01:01 Well, the horizontal asymptote is that horizontal line, which occurs right here when y is equal to negative 4, which means that a horizontal asymptote will be y equals negative 4...

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