Every rational function does NOT need to have holes. We can find the corresponding y-coordinates of the points by substituting the x-values in the simplified function. They can be obtained by setting the linear factors that are common factors of both numerator and denominator of the function equal to zero and solving for x. The holes of a rational function are points that seem that they are present on the graph of the rational function but they are actually not present. Apart from these, it can have holes as well. Now, we will solve this for x.Ī rational function can have three types of asymptotes: horizontal, vertical, and slant asymptotes. Set of all real numbers other than the values of y mentioned in the last step is the range.Įxample: Find the range of f(x) = (2x + 1) / (3x - 2).Set the denominator of the resultant equation ≠ 0 and solve it for y.If we have f(x) in the equation, replace it with y.To find the range of a rational function y= f(x): ![]() The range of a rational function is the set of all outputs (y-values) that it produces. Thus, the domain = Range of Rational Function We set the denominator not equal to zero.
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