0
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.
Add your answer:
Earn +20 pts
What do the asymptotes represent when you graph the tangent function?
When you graph a tangent function, the asymptotes represent x values 90 and 270.
Is it possible for graph of function to cross the horizontal assymptotes?
When you plot a function with asymptotes, you know that the graph cannot cross the asymptotes, because the function cannot be valid at the asymptote. (Since that is the point of having an asymptotes - it is a "disconnect" where the function is not valid - e.g when dividing by zero or something equally strange would occur). So if you graph is crossing an asymptote at any point, something's gone wrong.
How many non-verticle asymptotes can a rational function have?
Not sure what non-verticle means, but a rational function can have up to 2 non-vertical asymptotes,
Can a rational function have no vertical horizontal oblique asymptotes?
No, it will always have one.
How many asymptotes can a bounded function have?
I believe the maximum would be two - one when the independent variable tends toward minus infinity, and one when it tends toward plus infinity. Unbounded functions can have lots of asymptotes; for example the periodic tangent function.
What do the asymptotes represent when you graph the tangent function?
When you graph a tangent function, the asymptotes represent x values 90 and 270.
Is it possible for graph of function to cross the horizontal assymptotes?
When you plot a function with asymptotes, you know that the graph cannot cross the asymptotes, because the function cannot be valid at the asymptote. (Since that is the point of having an asymptotes - it is a "disconnect" where the function is not valid - e.g when dividing by zero or something equally strange would occur). So if you graph is crossing an asymptote at any point, something's gone wrong.
How many non-verticle asymptotes can a rational function have?
Not sure what non-verticle means, but a rational function can have up to 2 non-vertical asymptotes,
How many vertical asymptotes does the graph of this function have?
2
A sign chart helps you record data about a function's values around its and asymptotes?
A sign chart helps you record data about a function's values around its _____ and _____ asymptotes. zeros vertical
The vertical of the function secant are determined by the points that are not in the domain?
Asymptotes
Why are asymptotes important characteristics of rational functions?
Asymptotes are one way - not the only way, but one of several - to analyze the general behavior of a function.
Can a rational function have no vertical horizontal oblique asymptotes?
No, it will always have one.
To fill out a function's you will need to use test numbers before and after each of the function's and asymptotes.?
sign chart; zeros
How many asymptotes can a bounded function have?
I believe the maximum would be two - one when the independent variable tends toward minus infinity, and one when it tends toward plus infinity. Unbounded functions can have lots of asymptotes; for example the periodic tangent function.
A function has vertical asymptotes at x-values for which it is and near which the function's values become very positive or negative numbers?
Undefined; large
Limits in calculus?
A limit in calculus is a value which a function, f(x), approaches at particular value of x. They can be used to find asymptotes, or boundaries, of a function or to find where a graph is going in ambiguous areas such as asymptotes, discontinuities, or at infinity. There are many different ways to find a limit, all depending on the particular function. If the function exists and is continuous at the value of x, then the corresponding y value, or f (x), is the limit at that value of x. However, if the function does not exist at that value of x, as happens in some trigonometric and rational functions, a number of calculus "tricks" can be applied: such as L'Hopital's Rule or cancelling out a common factor.
