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Can the graph of a polynomial function have a vertical asymptote?
no
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
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.
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 asymptote of a circle?
A circle does not have an asymptote.
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.
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 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
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
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
How do you find asymptotes of any function?
Definition: If lim x->a^(+/-) f(x) = +/- Infinity, then we say x=a is a vertical asymptote. If lim x->+/- Infinity f(x) = a, then we say f(x) have a horizontal asymptote at a If l(x) is a linear function such that lim x->+/- Infinity f(x)-l(x) = 0, then we say l(x) is a slanted asymptote. As you might notice, there is no generic method of finding asymptotes. Rational functions are really nice, and the non-permissible values are likely vertical asymptotes. Horizontal asymptotes should be easiest to approach, simply take limit at +/- Infinity Vertical Asymptote just find non-permissible values, and take limits towards it to check Slanted, most likely is educated guesses. If you get f(x) = some infinite sum, there is no reason why we should be able to to find an asymptote of it with out simplify and comparison etc.
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.
