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Asymptotes Mind Map (Horizontal Asymptote (In class we studied two ways of…
Asymptotes Mind Map
Horizontal Asymptote
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The method used to find the horizontal asymptote changes depending on how the degrees of the polynomials in the numerator and denominator of the function compare.
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Vertical Asymptote
To find the vertical asymptote(s) of a rational function, simply set the denominator equal to 0 and solve for x.
The curves approach these asymptotes but never cross them. So the value that is given will tell us the number that the curve is approaching but will never touch
It's very easy to find the vertical asymptote since we just have to take in consideration the equation given and set 0 for all x in the equation and the result will give the value of the asymptote.
First of all, we have to think if we can 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 can not be:
This is the way in which we will find the value of the asymptote. So we get the equation of the denominator and then we solve and find the value that gives 0 since we cannot have a denominator of 0 in a fraction
So x cannot be 6 or –1, because then I'd be dividing by zero.