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VARVARA [1.3K]
3 years ago
10

How to find vertical asymptotes and horizontal asymptotes of a rational function?

Mathematics
1 answer:
irina1246 [14]3 years ago
7 0
A vertical asymptote occurs when the graph of a function approaches infinity as the independent variable approaches one or more specific rational values. This happens when the denominator of a fraction becomes zero. However, the fraction has to be in its simplest form (no common monomial factor between denominator and numerator).
A horizontal asymptote usually occurs for large positive or negative values of the independent variable where the function is a fraction and the polynomials forming the numerator and denominator have the same degree.
Example: y=(x+7)/(x-1) has a vertical asymptote at x=1 and a horizontal asymptote at y=1.
Example: y=(3x²+5x+9)/(x²-1) has a vertical asymptote at x=1 and at x=-1, and a horizontal asymptote at y=3.
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Step-by-step explanation:

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9) In the standard co-ordinate system, which of the following points in the greatest distance from origin? A. (-4, -1) B. (-3, 3
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The point with the greatest distance to the origin is given by:

B. (-3, 3).

<h3>What is the distance between two points?</h3>

Suppose that we have two points, (x_1,y_1) and (x_2,y_2). The distance between them is given by:

D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

The origin is given by point (0,0), hence the distance of a point (x,y) to the origin is given by:

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Hence the distances for each point given in the problem are:

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Hence option B has the greatest distance.

More can be learned about the distance between two points at brainly.com/question/18345417

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B*D?
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