The discontinuities of a rational function can be found by setting its denominator equal to zero and solving it. ... Hence, f is discontinuous at x=−2 and at x=3 .

Are rational functions continuous or discontinuous?

Every rational function is continuous everywhere it is defined, i.e., at every point in its domain. Its only discontinuities occur at the zeros of its denominator.

Do rational functions have extrema?

In conclusion, we have seen that a rational function with numerator and denominator of degree not more than two can have 0, 1, or 2 local extrema, and 0, 1, 2, or 3 points of inflection.