What does $f :[-3,3] \rightarrow \mathbb{R}$ mean? I don't understand what this means:
$f :[-3,3] \rightarrow \mathbb{R}$ defined by $f(x) = 3x^2 - 5x+1$
Does $[-3,3]$ describe an interval?
 A: Yes, but it is a degenerate interval consisting only of the single point {3}.
Edit: Editing this answer since the question has changed.
Interval notation typically uses square brackets to indicate inclusion of the corresponding endpoint and round brackets to indicate exclusion of the corresponding endpoint. Mixtures are allowed.
Thus, $[-3,3] = \{x\in\mathbb R : -3\leq x \leq 3\}$ includes both endpoints (called a "closed interval").
Likewise, $(-3,3) = \{x\in\mathbb R : -3< x < 3\}$ includes neither endpoint (called an "open interval").
The "half-open" interval $[-3,3) = \{x\in\mathbb R : -3\leq x < 3\}$ contains its left endpoint but not its right endpoint.
The "half-open" interval $(-3,3] = \{x\in\mathbb R : -3< x \leq 3\}$ contains its right endpoint but not its left endpoint.
Comment: Sometimes an outward-facing square bracket is used in place of a round bracket. Thus, $(-3,3)$ could be written $]-3,3[$. Similarly, $[-3,3)$ could be written $[-3,3[$. I personally find this notation somewhat disturbing because of its appearance as non-matching delimiters, but it is quite common.
