I have the function $\displaystyle f(a,b),U_{(a,b)})\rightarrow((c,d),U_{(c,d)})$, where $\displaystyle U_{(a,b)}$ is the subspace topology of the usual topology where A = (a,b) and $\displaystyle U_{(c,d)}$ is the subspace topology of the usual topology where A = (c,d), defined as $\displaystyle f(x)=\frac{d-c}{b-a}x+c-\frac{a(d-c)}{b-a}$

How do I show this function is continuous?