Answer
False
Work Step by Step
Let us assume that $A(x)$ and $B(x)$ as polynomials functions having degree of $m$ and $n$ respectively.
The rational function cab be defined as the quotient of two polynomials $A(x)$ and $B(x)$, that is, $\dfrac{A(x)}{B(x)}$. This can be discontinuous when the denominator becomes zero.
But the value of the denominator can only have a zero value for finitely many values of $x$.Thus, this can not have infinitely many values of $x$ at which the function is discontinuous.
Hence, the given statement is false.
