Answer
$W$ is not a subspace of $V=C[-1,1]$.
Work Step by Step
Let $W$ be a subset of $V$ such that
$$W=\{f : f(0)=-1\}, \quad V=C[-1,1].$$
$W$ is not a subspace of $V=C[-1,1]$ since it is not closed under scalar multiplication. For example, $f(x)=x-1\in W$ and $-2f(x)=-2(x-1)=-2x+2\not \in W$.