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A function y = f(x) has a vertical asymptote at x = c if,
f(x) is continuous for values of x just above c and the value of f(x) becomes infinitely large or infinitely negative (but not oscillating between them) as x approaches c from above. The function could behave similarly as x approaches c from below.
In such a case f(c) is a singularity: the function is not defined at that point.
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When a vertical asymptote is reflected over the x axis what does it become?
It remains a vertical asymptote. Instead on going towards y = + infinity it will go towards y = - infinity and conversely.
All rational functions have more than one vertical asymptote?
false
If a function has a vertical asymptote at a certain x-value then the function is at that value?
Undefined
How do I determine the domain and the equation of the vertical asymptote with the equation f of x equals In parentheses x plus 2 end of parentheses minus 1?
The domain of the function f(x) = (x + 2)^-1 is whatever you choose it to be, except that the point x = -2 must be excluded. If the domain comes up to, or straddles the point x = -2 then that is the equation of the vertical asymptote. However, if you choose to define the domain as x > 0 (in R), then there is no vertical asymptote.
Does every undefined value of fx lead to a vertical asymptote?
No. For example, in real numbers, the square root of negative numbers are not defined.
