The -intercept is the point where is the value substituted for that makes the value of the function equal to zero. A rational function can only equal zero when the numerator of the function is equal to zero. So set the numerator equal to zero and solve for the value of . That value will be the value of in the ordered pair describing the -intercept. Before you declare victory however, you need to make certain that the value you just computed does not also cause the denominator to be zero. In such an event, there is no -intercept for your function.
A rational function has a vertical asymptote described by the line where is any value that causes the denominator of the rational function to be equal to zero. So set the denominator of your function equal to zero and solve for the value of . That value is (or in some cases those values are) the value of in the equation(s) of the vertical asymptote(s).
