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) 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): -4 Horizontal asymptote(s): 2 (b) Find the domain and range of f. Write each answer as an interval or union of intervals. Domain: (-?, -4) ? (-4, ?) Range: (-?, 2) ? (2, ?) (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

          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): -4
Horizontal asymptote(s): 2

(b) Find the domain and range of f. Write each answer as an interval or union of intervals.

Domain: (-?, -4) ? (-4, ?)
Range: (-?, 2) ? (2, ?)

(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

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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) 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): -4
Horizontal asymptote(s): 2

(b) Find the domain and range of f. Write each answer as an interval or union of intervals.

Domain: (-?, -4) ? (-4, ?)
Range: (-?, 2) ? (2, ?)

(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

Added by Marcus P.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Gaurav Kalra

07/26/2022

Step 1

The vertical asymptote is at x = -4. ** Show more…

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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) 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): y-intercept(s):

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Transcript

00:01 Hi, first minute to find out the vertical asymptote here.

00:05 So, 4, the vertical asymptote.

00:09 The vertical asymptote, we have y is either infinity or y tends to negative infinity, right? if you see that here, y tends to infinity here, we have y tends to negative infinity, right? in the function, you can see that the y is infinity here or negative infinity.

00:26 So this line is the vertical asymptot.

00:28 This line is the vertical asymptote here, and that is given as x equal to minus 4.

00:32 Right, this is given as here, x equal to minus 4, that is the vertical asymptote.

00:40 Next we have horizontal asymptot.

00:47 Next we're given as the horizontal asymptot, right? so for horizontal asymptot we have here, it's going to be x is infinity or x is negative infinity, right? x infinity or x is negative infinity.

01:03 So here we have infinity or here we have negative infinity, right? so now this line here is the horizontal asymptote, right? and that is given as y equals 2.

01:15 So y equals 2 is the horizontal asymptot.

01:19 Next we have domain and range.

01:21 So for domain, domain is x values for which function is defined.

01:27 So you can see here the function is defined here we have from minus infinity to 4, right? and then 4 to infinity it is defined.

01:35 But 4 is not included.

01:36 So domain is coming out to be from negative infinity to negative 4, right? then we have union negative 4 to infinity, right? so that is the required domain...

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