Math Problem Statement
Solution
The graph in the image represents a "V"-shaped graph, which suggests it is the graph of an absolute value function. The function seems to have a vertex at , and the slopes of the two linear parts are different on either side of the vertex. Let's break this down.
Key observations:
- Vertex: The point is the lowest point, indicating that this is the vertex of the function.
- Slope:
- On the left of (from to ), the slope is .
- On the right of (from to ), the slope is .
General form of an absolute value function:
Where:
- is the vertex, so and .
- The slope is determined by the rate of change on either side of the vertex. Here, since the slopes are and .
Therefore, the equation of the function is:
Let me know if you need further clarification or details!
Here are five questions that build on this:
- What is the significance of the vertex in an absolute value function?
- How would the graph shift if we changed the equation to ?
- How does the slope change affect the shape of the graph?
- What would the equation be if the vertex were located at ?
- How do you interpret the impact of the constant in the absolute value function equation?
Tip: Always identify the vertex when working with absolute value functions—it helps set the foundation for the equation.
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Math Problem Analysis
Mathematical Concepts
Algebra
Absolute Value Functions
Graphing
Formulas
y = a|x - h| + k
Theorems
Properties of Absolute Value Functions
Suitable Grade Level
Grades 8-10
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