118k views
1 vote
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 PsyGnosis
by
7.2k points

1 Answer

1 vote

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.

__

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 Asle
by
8.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.