What is the relationship between the range and the equation of the asymptote
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1. User Answers Anonym
Vertical asymptotes are vertical lines which correspond to the zeroes of the denominator of a rational function. (They can also arise in other contexts, such as logarithms, but you'll almost certainly first encounter asymptotes in the context of rationals.) I'll give you an example:
This is a rational function. More to the point, this is a fraction. Can you have a zero in the denominator of a fraction? No. So if I set the denominator of the above fraction equal to zero and solve, this will tell me the values that x cannot be:
x2 – 5x – 6 = 0
(x – 6)(x + 1) = 0
x = 6 or –1So x cannot be 6 or –1, because then I'd be dividing by zero.
The domain is the set of all xvalues that I'm allowed to use. The only values that could be disallowed are those that give me a zero in the denominator. So I'll set the denominator equal to zero and solve.
x2 + 2x – 8 = 0
(x + 4)(x – 2) = 0
x = –4 or x = 2Since I can't have a zero in the denominator, then I can't have x = –4 or x = 2 in the domain. This tells me that the vertical asymptotes (which tell me where the graph can not go) will be at the values x = –4 or x = 2.
domain:
vertical asymptotes: x = –4, 2