An Asymptote is an instant line that constantly tactics a given curve but does no longer meet at an infinite distance.
According to the question;
asymptote: x = ±6
zero: x = 0
Explanation;
The vertical asymptotes of the function will be at the values of x where the denominator is zero. The denominator is x^2 -36, so has zeros for values of x that satisfy.
x^2 -36 = 0
x^2 = 36
x = ±√36 = ±6
The vertical asymptotes of the function are x = -6 and x = +6.
The zero of the function is at the value of x which makes the numerator zero. This will be the value of x that satisfies ...
6x = 0
x = 0 . . . . . divide by 6
The zero of the function is x=0.
A vertical asymptote of a graph is a vertical line x = a, in which the graph has a tendency in the direction of fine or bad infinity because of the inputs method a. A horizontal asymptote of a graph is a horizontal line y = b where the graph tactics the road as the inputs technique ∞ or –∞.
Learn more about asymptote here; https://brainly.com/question/4138300
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