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A vertical asymptote can be, but need not be a discontinuity. In simple terms, the distinction depends whether the domain extends on only one side of the (no discontinuity) or both sides (infinite discontinuity).
For example, there is no discontinuity in f(x) = 1/x for x > 0
On the other hand, f(x) = 1/x for x ≠0 has an infinite discontinuity at x = 0.
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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.
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.
Is it true that the function has a vertical asymptote at every x value where its numerator is zero and you can make a table for each vertical asymptote to find out what happens to the function there?
Every function has a vertical asymptote at every values that don't belong to the domain of the function. After you find those values you have to study the value of the limit in that point and if the result is infinite, then you have an vertical asymptote in that value
Can the graph of a rational function have more than one vertical asymptote?
Assume the rational function is in its simplest form (if not, simplify it). If the denominator is a quadratic or of a higher power then it can have more than one roots and each one of these roots will result in a vertical asymptote. So, the graph of a rational function will have as many vertical asymptotes as there are distinct roots in its denominator.
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
