1. **Problem Statement:** We are given a graph of a quadratic function with a restricted domain. The vertex is at $(-1,1)$ and the parabola opens upward starting from $x=-1$ extending to the right. 2. **Domain:** The domain is the set of all $x$ values for which the function is defined. Since the parabola starts at $x=-1$ and extends to the right, the domain is all $x$ such that $x \geq -1$. 3. **Expressing the domain in interval notation:** The domain is $[-1, \infty)$. 4. **Defining the function with an inequality for the restricted domain:** If the function is $f(x)$, then the domain restriction can be written as: $$x \geq -1$$ So the function is defined as $f(x)$ for $x \geq -1$. 5. **Summary:** - (a) Domain: $[-1, \infty)$ - (b) Domain restriction inequality: $x \geq -1$