Question

For \[f(x)=\frac{p(x)}{q(x)}\], where \[p(x)\] and \[q(x)\] are polynomial functions, where is \[f\] continuous?

Options

• Only where \[p(x)=0\]

• Only where \[q(x)=0\]

• Wherever it is defined, with \[q(x)\neq 0\]

• At no real number

Answer 1

A rational function \[f(x)=\frac{p(x)}{q(x)}\] is continuous wherever it is defined. Its domain excludes the values of \[x\] for which \[q(x)=0\].