https://file.aiquickdraw.com/mathbot/file/1726454641973z5h7yqx3.jpg

The given function is \( f(x) = -2|x + 1| + 4 \), which involves the absolute value function.

### Steps to sketch the graph:
1. **Basic Shape of Absolute Value Function:**
   - The base function is \( |x + 1| \), which is a V-shaped graph centered at \( x = -1 \), as the vertex of \( |x + 1| \) occurs where the expression inside the absolute value is zero (\( x = -1 \)).

2. **Reflection and Stretch:**
   - The coefficient \( -2 \) reflects the graph across the x-axis (flipping it upside down) and stretches it vertically by a factor of 2. This makes the "V" sharper and inverted.

3. **Vertical Shift:**
   - The \( +4 \) shifts the entire graph upwards by 4 units, moving the vertex of the graph to \( (-1, 4) \).

### Key Points:
- **Vertex:** The vertex of the graph is at \( (-1, 4) \).
- **Slope:** The slope of the left side of the graph (for \( x < -1 \)) is \( 2 \), and the slope of the right side (for \( x > -1 \)) is \( -2 \), due to the negative reflection.
  
### Sketch:
The graph forms a V-shape:
- It starts at \( (-1, 4) \).
- To the left of \( x = -1 \), it decreases with a slope of \( 2 \).
- To the right of \( x = -1 \), it decreases with a slope of \( -2 \) (due to reflection).

Would you like to see a detailed plot of the graph, or do you have any further questions?

### Related Questions:
1. How do you find the vertex of an absolute value function?
2. What happens to the graph when the coefficient of \( |x + 1| \) changes from \( 2 \) to \( -2 \)?
3. How do you determine the domain and range of \( f(x) = -2|x + 1| + 4 \)?
4. What effect does a vertical shift have on the graph of a function?
5. How can you derive the equation of an absolute value graph from its vertex?

**Tip:** Always start by identifying the vertex of an absolute value function, as it determines the basic shape and position of the graph.

Learn how to sketch the graph of the absolute value function f(x) = -2|x + 1| + 4. This lesson covers key transformations, including reflection and vertical shifts, and is suitable for 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