The "end behavior" of the function is that it approaches this asymptote as the value of x approaches ±∞.
According to the statement
we have to find that the relation of the asymptote with the given function.
So, For this purpose, we know that the
Asymptotes are lines the function approaches, but does not reach, as the independent variable nears some value. They may be horizontal, vertical, or slanted.
From the given information:
The function f is a f(x)=3x/x-9.
Then
Now, we discuss the vertical asymptotes
If a rational function has a denominator factor of (x -a) that is not matched by the same factor in the numerator, there will be a vertical asymptote at x=a.
The given function has a denominator factor of x-9 that does not appear in the numerator, so it has a vertical asymptote at x=0.
And then
Now, we discuss the horizontal asymptotes
As the magnitude of x gets large, the value of a rational function approaches the ratio of the highest-degree terms in the numerator and denominator. Here, that ratio is (3x)/(x) = 3. That is, the given function has a horizontal asymptote at y = 3.
So, The "end behavior" of the function is that it approaches this asymptote as the value of x approaches ±∞.
Learn more about asymptote here
https://brainly.com/question/3292510
#SPJ9
