https://file.aiquickdraw.com/mathbot/file/1726483519344zea38l6n.jpg

The graph in your image shows the equation \( y = \frac{1}{3} \sqrt{x} \), which is a transformation of the parent function \( y = \sqrt{x} \).

### Transformations of the Parent Function
The parent function is \( y = \sqrt{x} \), and the equation \( y = \frac{1}{3} \sqrt{x} \) represents a vertical compression. Specifically:
- The factor \( \frac{1}{3} \) compresses the graph vertically by a factor of \( \frac{1}{3} \), making it "flatter" compared to the parent function \( y = \sqrt{x} \).

### Visual Description:
- The graph should have the same basic shape as \( y = \sqrt{x} \), which starts at \( (0, 0) \) and gradually increases as \( x \) increases.
- The \( \frac{1}{3} \) multiplier causes the \( y \)-values to be scaled down. For instance, for a given \( x \), the output \( y \)-value will be one-third of the corresponding value in the parent function.

### Key Points to Consider:
- The parent function \( y = \sqrt{x} \) passes through points like \( (0, 0), (1, 1), (4, 2), (9, 3) \).
- The new function \( y = \frac{1}{3} \sqrt{x} \) will pass through the points \( (0, 0), (1, \frac{1}{3}), (4, \frac{2}{3}), (9, 1) \).

The graph you provided seems to reflect these points accurately, with the curve being less steep due to the vertical compression.

Would you like further clarification, or do you have any questions?

### Here are 5 related questions for further exploration:
1. How does a vertical stretch affect the graph of a function compared to a vertical compression?
2. What effect would multiplying the square root function by a negative value have on the graph?
3. What is the domain and range of the function \( y = \frac{1}{3} \sqrt{x} \)?
4. How would adding or subtracting a constant inside the square root affect the graph of the parent function?
5. Can you explain how horizontal shifts of the graph work for square root functions?

### Tip:
For square root functions, compressions and stretches only affect the vertical direction unless a transformation inside the square root is applied (which would affect the horizontal direction).

Graph the equation y = 1/3 * sqrt(x) by transforming the parent function y = sqrt(x).

This problem demonstrates how to graph the equation y = (1/3) sqrt(x), showing the transformation of the parent function y = sqrt(x) through vertical compression. Learn how the factor 1/3 affects the graph's shape and key points.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation