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What else can I help you with?
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.
Is a vertical asymptote undefined?
Yes, a vertical asymptote represents a value of the independent variable (usually (x)) where a function approaches infinity or negative infinity, and the function is indeed undefined at that point. This is because the function does not have a finite value as it approaches the asymptote. Thus, the vertical asymptote indicates a discontinuity in the function, where it cannot take on a specific 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.)
What is the vertical asymptote of 4 divided by x2?
2
If a function is positive at a test number it will remain positive until it reaches zero or a vertical asymptote?
true
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.
Is a vertical asymptote undefined?
Yes, a vertical asymptote represents a value of the independent variable (usually (x)) where a function approaches infinity or negative infinity, and the function is indeed undefined at that point. This is because the function does not have a finite value as it approaches the asymptote. Thus, the vertical asymptote indicates a discontinuity in the function, where it cannot take on a specific value.
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
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.
Do logarithmic functions have vertical asymptotes?
Yes. Take the functions f(x) = log(x) or g(x) = ln(x) In both cases, there is a vertical asymptote where x = 0. Because a number cannot be taken to any power so that it equals zero, and can only come closer and closer to zero without actually reaching it, there is an asymptote where it would equal zero. Note that transformations (especially shifting the function left and right) can change the properties of this 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.
What is the vertical asymptote of 4 divided by x2?
2
