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To solve for asymptotes of a function, you typically look for vertical, horizontal, and oblique asymptotes. Vertical asymptotes occur where the function approaches infinity, typically at values where the denominator of a rational function is zero but the numerator is not. Horizontal asymptotes are determined by analyzing the behavior of the function as it approaches infinity; for rational functions, this involves comparing the degrees of the polynomial in the numerator and denominator. Oblique asymptotes occur when the degree of the numerator is one higher than that of the denominator, and can be found using polynomial long division.
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Can a slant asymptote cuts the graph?
No. If it cuts a graph it is not an asymptote.
What is the asymptote of 3x?
It has no asymptote. 3x is a straight line and therefore is a tangent to itself.
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?
What is the vertical asymptote of 4 divided by x2?
2
What is the asymptote of a circle?
A circle does not have an asymptote.
Can a slant asymptote cuts the graph?
No. If it cuts a graph it is not an asymptote.
When was Asymptote Architecture created?
Asymptote Architecture was created in 1989.
What is an asymptote?
An asymptote is a line or curve that approaches a given curve arbitrarily closely.
Does every rational function have an asymptote?
No if the denominators cancel each other out there is no asymptote
What is the asymptote of 3x?
It has no asymptote. 3x is a straight line and therefore is a tangent to itself.
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 is the vertical asymptote of 4 divided by x2?
2
What did the derivative near the horizontal asymptote shout to the derivative near the vertical asymptote?
I don't know, what?
When was Asymptote - vector graphics language - created?
Asymptote - vector graphics language - was created in 2004.
Does y equals log5x have an asymptote?
Yes, the asymptote is x = 0. In order for logarithmic equation to have an asymptote, the value inside log must be 0. Then, 5x = 0 → x = 0.
What are the asymptotes of a linear function?
Considering an asymptote as a tangent to the curve "at infinity", the asymptote is the straight line itself.
