Question

The statement, "A rational function is continuous for all real numbers." isA.true for all rational functions.B.true for some rational functions.C.never true for rational functions.

Answer 1

A rational function is a function that can be written in the form p(x)/q(x), where p(x) and q(x) are polynomials of x and q(x)≠0.

A rational function is not defined at values of x where the denominator of the function becomes zero. So, a rational function may or may not be defined at all real numbers.

A rational function will be continuous at points in the domain of the function.

Since a rational function need not be defined at all real numbers, the function need not be continuous at all real numbers.

Therefore, the statement "A rational function is continuous for all real numbers" is true for only some rational functions".

So, option B is correct.