Question: I have the following graph:

$$h(t) = \begin{cases} 2t+1, & \mathrm{if}\ t \le -1, \\
3t, & \mathrm{if}\ -1 < t < 1, \\
2t-1, & \mathrm{if}\ t \ge 1.\end{cases}$$

The question I have to answer is: Give the conditions which would make the function $h$ continuous at the point $t = a$.

This question does not make sense to me. Firstly there is no a in the equation, and secondly it does not matter what value i would give to $t$, this function can never be continuous.

Do I misunderstand what is required here?

Answer: 
The question asks for the conditions (on $a$) which make the function continuous **at** $t=a$. I think you know the answer. 

The function is not continuous at $t=-1$. (Perhaps in your answer you should explain how you know this.) It is not continuous at $t=1$. It is continuous at $t=a$ for any value of $a$ **other than** $-1$ or $1$. (Perhaps you should explain how you know that.)
so conditions would be that limit of left and right side of function would be same,also $h(a)$ exist and is equal to limit of left and right side;