[tex]f(x)=
\begin{cases}
-2&x\le -1\\
ax-b&-1\ \textless \ x\ \textless \ 1\\
3&x\ge 1
\end{cases}[/tex]
notice, is a piecewise
continuity for a piecewise means
one subfunction has to pick up where the previous one left off
so...if we look at the first subfunction
f(x) = -2 <-- that's a horizontal line up to the point of x = -1
so... whatever ax+b is, must be -2 also when x = -1
the subfunction following ax+b is
f(x) = 3 <--- another horizontal line, from the point x = 1 onwards
so... whatever ax+b is, must be 3 when x = 1
so f(x) = 3 picks up at that point
is that making any sense?
