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By checking the values for a function on only one side of its asymptote you can know for sure how the graph should look?
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∙ 13y ago
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∙ 13y ago
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Is it true that you should always check a function's values on both sides of its asymptote?
It is often a good idea. But consider this: it may not have a value on the wrong side of the asymptote. Try graphing y = 1/x.
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.
For all values of a and b that make Fx equals a bx a valid exponential function the graph always has a horizontal asymptote at y equals 0?
True
How can you find the domain and range of a function?
The domain is a subset of the values for which the function is defined. The range is the set of values that the function takes as the argument of the function takes all the values in the domain.
What are limits in maths?
Limits (or limiting values) are values that a function may approach (but not actually reach) as the argument of the function approaches some given value. The function is usually not defined for that particular value of the argument.
Is it true that you should always check a function's values on both sides of its asymptote?
It is often a good idea. But consider this: it may not have a value on the wrong side of the asymptote. Try graphing y = 1/x.
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 the meaning of asymptote?
An asymptote is the tendency of a function to approach infinity as one of its variable takes certain values. For example, the function y = ex has a horizontal asymptote at y = 0 because when x takes extremely big, negative values, y approaches a fixed value : 0. Asymptotes are related to limits.
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.
For all values of a and b that make Fx equals a bx a valid exponential function the graph always has a horizontal asymptote at y equals 0?
True
What is vertical asymptote?
A function y = f(x) has a vertical asymptote at x = c if,f(x) is continuous for values of x just above c and the value of f(x) becomes infinitely large or infinitely negative (but not oscillating between them) as x approaches c from above. The function could behave similarly as x approaches c from below.In such a case f(c) is a singularity: the function is not defined at that point.
Why are the y-values of an exponential growth function either always greater than or less than the asymptote of the function?
The exponential function is always increasing or decreasing, so its derivative has a constant sign. However the function is solution of an equation of the kind y' = ay for some constant a. Therefore the function itself never changes sign and is MORE?
How do you find an oblique asymptotes?
An oblique asymptote is another way of saying "slant asymptote."When the degree of the numerator is one greater than the denominator, an equation has a slant asymptote. You divide the numerator by the denominator, and get a value. Sometimes, the division pops out a remainder, but ignore that, and take the answer minus the remainder. Make your "adapted answer" equal to yand that is your asymptote equation. To graph the equation, plug values.
Which function has no horizontal asymptote?
Many functions actually don't have these asymptotes. For example, every polynomial function of degree at least 1 has no horizontal asymptotes. Instead of leveling off, the y-values simply increase or decrease without bound as x heads further to the left or to the right.
How do you know when a function has a vertical asymptote?
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.
Why function should return a value?
Not all functions return values. If you take a function which is of type void, you get a function which is does not return anything. The only functions which should return values are those which are used as a right side of expressions (so called rvalues).
What are the domain and range of the function?
The domain of a function is the set of values for which the function is defined.The range is the set of possible results which you can get for the function.
