Question

How do you find the discontinuity of a rational function ?

Answer 1

Hint: In the given question, we are asked to find the condition for which a rational number may be discontinuous. A rational function is a function that consists of a function in the rational format just like the rational numbers. The rational numbers are the numbers that can be represented in the \[\left( {\dfrac{p}{q}} \right)\] form where p and q belong to the real number set and q is not equal to zero.

Complete step by step solution:
So, in the given question, we are required to find the reason for discontinuity of a rational function. A rational number is a number that can be represented in the
\[\left( {\dfrac{p}{q}} \right)\] form where p and q belong to the real number set and q is not equal to zero.
Similar to the rational numbers, the rational functions are functions of
\[\left( {\dfrac{p}{q}} \right)\] form where p and q are expressions in a variable, say x.
Hence, if the expressions p and q yield non real values, the rational function may be discontinuous and if denominator expression q equals to zero for any value of variable, then the rational function is undefined for that particular value of variable, and this leads to discontinuity.

Note: Rational functions are functions with a numerator and denominator. For the continuity of the rational functions, p and q expressions in the variable must yield values in the set of real numbers and the denominator expression, q must not be equal to zero for any value of variable, x.