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Find the​ vertical, horizontal, and oblique​ asymptotes, if​ any, for the following rational function.
T(x) = 2x²/x²-4x+3
Find the vertical​ asymptote(s), if​ any, of the function.
A. The vertical​ asymptote(s) is/are____.
B. There is no vertical asymptote.
Find the horizontal​ asymptote(s), if​ any, of the function.
A. The horizontal​ asymptote(s) is/are____.
B. There is no horizontal asymptote.
Find the oblique​ asymptote(s), if​ any, of the function.
A. The oblique​ asymptote(s) is/are____.
B. There is no oblique asymptote

Sagot :

Answer:

Vertical Asymptote - A

Horizontal Asymptote - A

Oblique - B

Step-by-step explanation:

To find the vertical asymptote, we can simply factorize the denominator of the function. Doing this, we get (x-1) and (x-3). Our vertical asymptotes are at x=1 or 3.

Because the top and bottom exponents of the leading coefficient ( the number with the highest degree or something) are the same, both are 2, the horizontal asymptote is those two numbers divided, so we get 2 as our horizontal asymptote.

There is no oblique asymptote. the numerator's degree ≠ 1 + denominator's degree, so there is no oblique or slant asymptote.

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