Is \(f(x)=x^2+1\) continuous at \(x=2\)?

Is \(g(x)=\frac{1}{x-3}\) continuous at \(x=3\)?

Determine whether \(f(x)=\frac{x^2-1}{x-1}\) is continuous at \(x=1\).

Let \(f(x)=x+2\) for \(x<1\), and \(f(x)=4\) for \(x\ge1\). Is \(f\) continuous at \(x=1\)?

Find \(k\) so that \(f(x)=kx+1\) for \(x<2\), and \(f(x)=7\) for \(x\ge2\), is continuous at \(x=2\).

Define \(f(x)=\frac{x^2-4}{x-2}\) for \(x\ne2\). What value should be assigned to \(f(2)\) to make \(f\) continuous at \(x=2\)?

For \(f(x)=\sqrt{x-5}\), state where \(f\) is continuous.

Let \(f(x)=x^2\) for \(x\le0\), and \(f(x)=ax+b\) for \(x>0\). If \(f\) is continuous at \(0\) and \(f(1)=3\), find \(a\) and \(b\).

Classify the discontinuity of \(f(x)=\frac{x+1}{x^2-1}\) at \(x=1\) and at \(x=-1\).

Let \(f(x)=\frac{x^2-ax}{x-a}\) for \(x\ne a\), where \(a\ne0\). What value of \(f(a)\) makes \(f\) continuous at \(x=a\)?