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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.
What is the vertical asymptote of 4 divided by x2?
2
True or False if a rational function Rx has exactly one vertical asymptote then the function 3Rx should have the exact same asymptote?
It will have the same asymptote. One can derive a vertical asymptote from the denominator of a function. There is an asymptote at a value of x where the denominator equals 0. Therefore the 3 would go in the numerator when distributed and would have no effect as to where the vertical asymptote lies. So that would be true.
What did the derivative near the horizontal asymptote shout to the derivative near the vertical asymptote?
I don't know, what?
Can the graph of a polynomial function have a vertical asymptote?
no
How do you find vertical asymptote?
One way to find a vertical asymptote is to take the inverse of the given function and evaluate its limit as x tends to infinity.
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.
Why doesnt the graph of a rational function cross its vertical asymptote?
It can.
Can the graph of a function have a point on a vertical asymptote?
No. The fact that it is an asymptote implies that the value is never attained. The graph can me made to go as close as you like to the asymptote but it can ever ever take the asymptotic value.
All rational functions have more than one vertical asymptote?
false
Why doesn't a rational function not need at least one vertical asymptote?
That is not correct. A rational function may, or may not, have a vertical asymptote. (Also, better don't write questions with double negatives - some may find them confusing.)
What is A line that a graph approaches but does not reach It may be a vertical horizontal or slanted line?
It is an asymptote.
If a function has a vertical asymptote at a certain x-value then the function is at that value?
Undefined
