The equation shown in the image is:

$y = x^2 + 2$

To find the domain and range:

Domain:

The domain of a function is the set of all possible input values (i.e., $x$-values). In this case, since there are no restrictions on $x$ (like square roots or denominators that could make the expression undefined), the domain is:

$\text{Domain: } (-\infty, \infty) \quad \text{or} \quad \mathbb{R}$

Range:

The range of a function is the set of all possible output values (i.e., $y$-values). The given equation is a quadratic function of the form $y = x^2 + 2$. The graph of $y = x^2 + 2$ is a parabola that opens upwards, with its vertex at $y = 2$ (since the minimum value of $x^2$ is 0, and $x^2 + 2$ will always be greater than or equal to 2).

Thus, the range is:

$\text{Range: } [2, \infty)$

Would you like further details or explanations on these steps?

Related Questions:

1. How can we graph the function $y = x^2 + 2$?
2. How do we determine if a function is one-to-one or onto?
3. What would be the effect of changing the equation to $y = x^2 - 2$?
4. How can we find the vertex of a quadratic function?
5. What are the differences between domain and range in other types of functions?

Tip: For quadratic functions in the form $y = ax^2 + bx + c$, the vertex and direction of the parabola can help determine the range!