https://file.aiquickdraw.com/mathbot/file/1726370454566r5xpgvkc.jpg

What is the domain and range of the graph as well as the parent function

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.

What is the domain and range of the graph as well as the parent function?

Explore the domain and range of the square root function, f(x) = √x, based on its graph. Understand key mathematical concepts and formulas, including how the domain starts at x ≥ 0 and the range is y ≥ 0. Perfect for Grades 9-10 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation