https://file.aiquickdraw.com/mathbot/file/1726588198098x26rwobv.jpg

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!

Learn how to find the domain and range of the quadratic function y = x^2 + 2. This step-by-step guide explains the key concepts behind quadratic functions, suitable for Grades 7-10. Understand the domain as all real numbers and the range starting from y = 2 to infinity.

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