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Can a value of X cross a horizontal asymptote of a rational function sometimes?
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Yes.
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∙ 11y ago
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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.
What is the formula for a rational function with x intercepts at x equals 3 and x equals negative 2. y intercept at y equals 12. a hole at x equals 1 and no horizontal asymptote?
f(x) = 2*(x-3)*(x+2)/(x-1) for x ≠1
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.
What is a rational function graph?
The Equation of a Rational Function has the Form,... f(x) = g(x)/h(x) where h(x) is not equal to zero. We will use a given Rational Function as an Example to graph showing the Vertical and Horizontal Asymptotes, and also the Hole in the Graph of that Function, if they exist. Let the Rational Function be,... f(x) = (x-2)/(x² - 5x + 6). f(x) = (x-2)/[(x-2)(x-3)]. Now if the Denominator (x-2)(x-3) = 0, then the Rational function will be Undefined, that is, the case of Division by Zero (0). So, in the Rational Function f(x) = (x-2)/[(x-2)(x-3)], we see that at x=2 or x=3, the Denominator is equal to Zero (0). But at x=3, we notice that the Numerator is equal to ( 1 ), that is, f(3) = 1/0, hence a Vertical Asymptote at x = 3. But at x=2, we have f(2) = 0/0, 'meaningless'. There is a Hole in the Graph at x = 2.
When you are given a graph how can you come up with a rational function equation?
You cannot, necessarily. Given a graph of the tan function, you could not.
Does every rational function has at least one horizontal asymptote?
Nope not all the rational functions have a horizontal asymptote
Can the graph of a rational function have both a horizontal and oblique asymptote?
Piece wise functions can do everything. Take two pieces of two rational functions, one have a horizontal asymptote as x goes to -infinity and the other have a slanted (oblique) one as x goes to +infinity. It is still a rational function.
Does every rational function have an asymptote?
No if the denominators cancel each other out there is no asymptote
How do you find the horizontal asymptote in a graph of a rational function?
The horizontal asymptote is what happens when x really large. To start with get rid of all the variables except the ones with the biggest exponents. When x is really large, they are the only ones that will matter. If the remaining exponents are the same, then the ratio of those coefficients tell you where the horizontal asymptote is. For example if you have 2x3/3x3, then the ratio is 2/3 and the asymptote is f(x)=2/3 or y=2/3. If the exponent in the denominator is bigger, than y=0 is the horizontal asymptote. If the exponent in the numerator is bigger, than there is no horizontal asymptote.
Why doesnt the graph of a rational function cross its vertical asymptote?
It can.
If a function has a vertical asymptote at a certain x-value then the function is at that value?
Undefined
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.)
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.
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.
Given the rational function 2x-3x2 -5x-6 find the verticle and horizontal asymptotes?
f(x) = (2x - 3x2)/(-5x - 6)f(x) = -(3x2 - 2x)/-(5x + 6)f(x) = (3x2 - 2x)/(5x + 6)5x + 6 = 05x + 6 - 6 = 0 - 65x = -65x/5 = -6/5x = -6/5 (the vertical asymptote of f)Since the degree of the polynomial function in the numerator is greater than the degree of the polynomial function in the denominator, then the graph of f has no horizontal asymptote.
Can a rational function have no vertical horizontal oblique asymptotes?
No, it will always have one.
Does every rational function have more than one vertical asymp tote?
No.The equation x/(x^2 + 1) does not have a vertical asymptote.
