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Find the asymptote(s) if the graph of the function. Select all that apply.

x = -2
x = -1
x = 1
y = 0

Find the asymptote(s) if the graph of the function. Select all that apply. x = -2 x-example-1
User Brettski
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1 Answer

24 votes
24 votes

Answer:

(a) x = -2

(d) y = 0

Explanation:

You want the asymptote(s) of the graph of the function.

Asymptotes

An asymptote is a value that a function approaches, but never reaches. Asymptotes may be horizontal, vertical, or "slant", and are often associated with exponential, log, or rational functions.

Application

The graph shows a vertical asymptote at x = -2. The graph approaches -∞ as x approaches -2 from the left, and it approaches +∞ as x approaches -2 from the right.

The graph shows a horizontal asymptote at y = 0. The graph approaches 0 as x takes on large negative values.

The asymptotes of the graph are x = -2 and y = 0.

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Additional comment

An exponential function will have an asymptote at y=0. A log function will have an asymptote at x=0. Rational functions will have vertical asymptotes where denominator zeros are not matched by numerator zeros. (Matched zeros result in a "hole" in the graph.)

A rational function will have a horizontal asymptote when the numerator degree is equal to or less than the denominator degree. There will be a "slant" asymptote when the numerator has degree one higher than the denominator.

User Cashew
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