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Vertical asymptotes occur when the denominator of a rational function is zero. Since we cannot divide by zero, but we can get very close to zero on either side of it, this creates an asymptote.
There are other times such as logs when they occur, but rational functions are the ones mostly commonly seen in math classes.
So the simplest of examples would be 1/x. Since we cannot divide by 0, x cannot be 0, but it can be 1/10000000 or 1/10000000000000. It can also be -1/10000 or -1/1000000000. In other words, we can get as close to zero from either the right or the left as we want. The line x=0 forms a vertical asymptote.
Now if we make the function 1/(1-x), we have the same situation where if x=1, the denominator becomes 1-1=0. So we can get as close to 1 from the right or the left and the line x=1 forms a vertical asymptote.
So the bottom line ( pun intended) is if the denominator of a rational function becomes zero with certain values of x, say x=m, then the line x=m is a vertical asymptote.
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Does every rational function have more than one vertical asymp tote?
No.The equation x/(x^2 + 1) does not have a vertical asymptote.
The horizontal asymptote for exponential function is?
The graph of an exponential function f(x) = bx approaches, but does not cross the x-axis. The x-axis is a horizontal asymptote.
Should you check the value of a function on its asymptote to get a good idea of how its graph should look?
The asymptote is a line where the function is not valid - i.e the function does not cross this line, in fact it does not even reach this line, so you cannot check the value of the function on it's asymptote.However, to get an idea of the function you should look at it's behavior as it approaches each side of the asymptote.
How do you find the vertical asymptote for the logarithmic function f of x equals log x?
The only way I ever learned to find it was to think about it. The function f(x) = log(x) only exists of 'x' is positive. As 'x' gets smaller and smaller, the function asymptotically approaches the y-axis.
Can a value of X cross a horizontal asymptote of a rational function sometimes?
Yes.
Can the graph of a polynomial function have a vertical asymptote?
no
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 doesnt the graph of a rational function cross its vertical asymptote?
It can.
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.
If a function has a vertical asymptote at a certain x-value then the function is at that value?
Undefined
What did the derivative near the horizontal asymptote shout to the derivative near the vertical asymptote?
I don't know, what?
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
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.)
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.
What is the vertical asymptote of 4 divided by x2?
2
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.
If a function is positive at a test number it will remain positive until it reaches zero or a vertical asymptote?
true
