The graph you uploaded shows a curve that looks like part of a square root function. To answer your questions:

Parent Function

The curve resembles the graph of the square root function: $f(x) = \sqrt{x}$ This is the parent function of the square root family of functions.

Domain

The domain of the square root function consists of all values for which the expression inside the square root is non-negative (since we can't take the square root of negative numbers in the real number system). For this function, the domain is: $x \geq 0$ So, the domain of the function is: $\boxed{[0, \infty)}$

Range

The range of a square root function consists of all non-negative values of $y$ since the square root always produces non-negative outputs. Therefore, the range is: $y \geq 0$ Thus, the range of the function is: $\boxed{[0, \infty)}$

Summary:

• Parent function: $f(x) = \sqrt{x}$
• Domain: $[0, \infty)$
• Range: $[0, \infty)$

Would you like more details or explanations? Here are five questions to explore further:

1. How does shifting the square root function affect its domain and range?
2. What is the difference between the domain and range of $f(x) = \sqrt{x}$ and $f(x) = x^2$?
3. How can we find the domain of more complex functions involving square roots?
4. What happens to the graph of the square root function when you multiply it by a constant?
5. How can you reflect the square root function across the x-axis or y-axis?

Tip: When determining the domain of functions involving square roots, always check when the expression inside the root is non-negative.