The intercepts of a function are the values of x when f(x) = 0 and the value of f(x) when x = 0, corresponding to the coordinate values of x and y where the graph of the function crosses the x and yaxes. Find the yintercept of a rational function as you would for any other type of function: plug in x = 0 and solve. Find the xintercepts by factoring the numerator. Remember to exclude holes and vertical asymptotes when finding the intercepts.

Plug the value x = 0 into the rational function and determine the value of f(x) to find the yintercept of the function. For example, plug x = 0 into the rational function f(x) = (x^2  3x + 2) / (x  1) to get the value (0  0 + 2) / (0  1), which is equal to 2 / 1 or 2 (if the denominator is 0, there is a vertical asymptote or hole at x = 0 and therefore no yintercept). The yintercept of the function is y = 2.

Factor the numerator of the rational function completely. In the above example, factor the expression (x^2  3x + 2) into (x  2)(x  1).

Set the factors of the numerator equal to 0 and solve for the value of the variable to find the potential xintercepts of the rational function. In the example, set the factors (x  2) and (x  1) equal to 0 to get the values x = 2 and x = 1.

Plug the values of x you found in Step 3 into the rational function to verify that they are xintercepts. Xintercepts are values of x that make the function equal to 0. Plug x = 2 into the example function to get (2^2  6 + 2) / (2  1), which equals 0 / 1 or 0, so x = 2 is an xintercept. Plug x = 1 into the function to get (1^2  3 + 2) / (1  1) to get 0 / 0, which means there is a hole at x = 1, so there is only one xintercept, x = 2.
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