I forgot how to look for the asymptote from an equation.. can someone please help me out?
example: y= x/(x+1) what's the asymptote in this case?
Thanks.
A vertical asymptote is located where the denominator vanishes. In the cited example, the denominator has a zero at x=-1, where the vertical asymptote would be located.
The horizontal asymptote, if it exists, is obtained by dividing the leading coefficient of the numerator by that of the denominator. A leading coefficient is the coefficient of the highest term of a polynomial. In the example, both have a coefficient of 1, so the horizontal asymptote is at y=1.
Post if you need further clarifications.
Of course! To find the asymptote of a function, you'll need to follow these steps:
1. Determine the degree of the numerator and denominator of the rational function. In your example, the numerator, x, is of degree 1, and the denominator, x+1, is also of degree 1.
2. If the degree of the numerator is less than the degree of the denominator, there will be a horizontal asymptote at y = 0. However, if the degrees are equal, or if the degree of the numerator is greater, you'll need to perform further calculations.
3. Divide the numerator by the denominator using a suitable method such as long division or synthetic division. In the case of your example, using long division: divide x by x+1.
x / (x+1) = 1 - 1/(x+1)
4. After performing the division, you'll have a new expression. In this case, it simplifies to 1 - 1/(x+1).
5. Examine the simplified expression. The denominator (x+1) indicates a vertical asymptote at x = -1. This means that the graph of the function will approach infinity as it gets closer to x = -1 from both sides.
So, in your example, the vertical asymptote is x = -1. Remember to check for both horizontal and vertical asymptotes whenever dealing with rational functions.