Hi,
If you were given, say: x-intercept of -4, y-intercept of -2, vertical asymptote x=2, and horizontal asymptote y=1. How do you find the equation for a rational function with these features?
Thanks in advance.
The simplest model to use is $\displaystyle y = \frac{a}{x - b} + c$. Your job is to find the values of a, b and c using the given information. You will get an answer equivalent to skeeter's.
In fact, the only information required is vertical asymptote x=2, horizontal asymptote y=1 and y-intercept of -2. The information x-intercept of -4 can be used to check your answer.
To supplement to Mr. Fantastic's information: horizontal asymptotes occur in the numerator and vertical asymptotes occur in denominator. If you recall a function cannot cross an asymptote (always in the case of vertical, most times true in the case of horizontal). Which means that the function cannot be a certain value there.
Thus, if a vertical asymptote of 2 exists we must have (x - 2) in the denominator.
Also recall that at the x-intercept y = 0, thus we must have (x+4) in the numerator because our x-intercept of -4 makes this equation 0.