I am having a midterm review in school and there's one concept that I forgot how to solve, and that is solving for continuous functions?
More precisely, what does a variable have to be for the following to be continuous. For example, the problem I am dealt with solving is $F(x)=\left\{\begin{array}{ll} 2x&\text{if }x\leq 1\\ ax^2+1&\text{if }x\gt 1\\ \end{array}\right.$ and I have to solve for $a$. Normally, I would solve for $ax^2+1$, but I know that is wrong. Can someone tell me how to solve this, and perhaps by using a different problem so that I may be able to do the one I have on my own?