The graph provided represents a V-shaped function typical of an absolute value function. To write an equation that matches this graph, we need to consider the following characteristics:

1. Vertex of the graph: The point where the V-shape turns.
2. Slope of the lines: The steepness of each "arm" of the V-shape.
3. Horizontal and vertical shifts: Any movement of the function away from the origin.

Let's denote the general form of an absolute value function:

$y = a |x - h| + k$

where:

• $(h, k)$ is the vertex of the graph.
• $a$ is a multiplier that affects the slope of each arm.

Steps to Formulate the Equation:

1. Locate the Vertex: Determine the coordinates of the vertex on the graph. Suppose the vertex is at $(h, k)$.

2. Determine the Slope: Observe the slope of the arms (both left and right) to find the value of $a$.

3. Equation Formulation: Substitute the values of $h$, $k$, and $a$ into the formula $y = a |x - h| + k$.

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If you can share the specific coordinates or any other features observed from the graph, I can provide the exact equation. Otherwise, the structure above provides the template for writing the absolute value equation.

Would you like more details on any of these steps?

Related Questions

1. How does the value of $a$ affect the steepness of the absolute value graph?
2. What transformations occur if we change the value of $h$ in $y = a |x - h| + k$?
3. How does adding a constant $k$ outside the absolute value affect the graph’s position?
4. Can an absolute value function have a negative slope on one side? If yes, how is that represented?
5. What are the similarities and differences between absolute value graphs and linear graphs?

Tip:

When working with absolute value graphs, always identify the vertex first; it provides a foundation for understanding the entire function.