raph the equation shown below by transforming the given graph of the parent function.

y, equals, open vertical bar, x, minus, 2, close vertical bar

*y*=∣*x*−2∣

To graph the equation \( y = |x - 2| \), you can start with the graph of the parent function \( y = |x| \) and apply the necessary transformation.

### Steps to Graph \( y = |x - 2| \):

1. **Parent Function:**  
   The parent function is \( y = |x| \), which is a V-shaped graph with the vertex at the origin (0, 0). The graph opens upwards, with the left side having a slope of -1 and the right side having a slope of 1.

2. **Horizontal Shift:**  
   The equation \( y = |x - 2| \) represents a horizontal shift of the parent function \( y = |x| \). Specifically, the graph will be shifted **2 units to the right**. 
   
   - **Vertex:** The new vertex of the graph will be at (2, 0) instead of (0, 0).
   - The V-shape remains the same, with the graph still opening upwards. The slopes of the lines on either side of the vertex are unchanged.

3. **Plotting the Graph:**
   - Start by plotting the vertex at the point (2, 0).
   - Then, draw the lines with a slope of 1 to the right of the vertex and -1 to the left of the vertex.

### Graph Description:
- The vertex of the graph is at \( (2, 0) \).
- The left side of the graph decreases linearly with a slope of -1 as \( x \) decreases from 2.
- The right side of the graph increases linearly with a slope of 1 as \( x \) increases from 2.

### Graph Representation:
If you were to plot this on a coordinate plane, it would look like this:

- The vertex at \( (2, 0) \).
- The line extends downward to the left and upward to the right, creating a V-shape.

Would you like to see the graph drawn or have further details on how the transformation was applied?

---

**5 Related Questions:**
1. How would the graph change if the equation were \( y = |x + 2| \)?
2. What effect does multiplying the absolute value function by a constant have on the graph?
3. How would you graph \( y = |x - 2| + 3 \)?
4. How does the graph of \( y = |x - 2| \) compare to the graph of \( y = -|x - 2| \)?
5. What is the vertex form of an absolute value function?

**Tip:** For any transformation, always identify the type of transformation (e.g., translation, reflection, dilation) and its effect on the graph’s key features like the vertex and slope.

Learn how to graph the absolute value function |x - 2| with a step-by-step guide. Understand the effect of horizontal shifts on the graph of the absolute value function. Suitable for high school 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