https://file.aiquickdraw.com/mathbot/file/1726752121295x7689ogc.jpg

The question asks you to identify the equation of \( h(x) \) that represents the given graph.

### Steps to Analyze:

1. **Graph Overview**: 
   - The graph appears to resemble a square root function, which is typically of the form \( y = \sqrt{x} \), but the curve is shifted.
   - The graph starts at \( (1, 2) \), suggesting there is a transformation (translation) involved.

2. **Transformation Details**:
   - **Shift in the x-direction**: The graph does not start at \( (0, 0) \), but at \( (1, 2) \), implying a horizontal shift. If the function is in the form \( y = \sqrt{x - h} \), the graph would shift horizontally by \( h \).
   - **Shift in the y-direction**: The starting value of \( y \) is 2 at \( x = 1 \), which suggests a vertical shift upwards by 2.

3. **Checking the Answer Options**:
   Based on the shifts described, the correct function should reflect both a horizontal shift by 1 and a vertical shift by 2. Thus, the equation will take the form:
   \[
   h(x) = \sqrt{x - 1} + 2
   \]

### Correct Answer:
The equation that represents the graph is:
- \( h(x) = \sqrt{x - 1} + 2 \)

Let me know if you would like a more detailed explanation or further questions related to this!

---

Here are 5 relative questions:
1. How do you identify vertical and horizontal shifts in square root functions?
2. What are the general transformations applied to a square root function?
3. How would the graph change if the equation was \( h(x) = \sqrt{x + 1} + 2 \)?
4. What effect does multiplying the square root by a constant have on the graph?
5. How do you find the domain of the square root function \( h(x) = \sqrt{x - 1} + 2 \)?

**Tip**: Always check the graph's starting point (domain) and shape when identifying transformations of root functions.

Identify the equation of h(x) that represents the given graph.

Learn how to identify the equation of a square root function from its graph. This problem involves recognizing horizontal and vertical shifts, with the final equation h(x) = √(x - 1) + 2. Suitable for high school students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation