Math Problem Statement
Solution
The graph displayed is a V-shaped function, which is characteristic of an absolute value function. From the graph, we can observe the following:
- The vertex of the graph is at , which indicates a vertical shift downward by 1.
- The graph opens downward, suggesting that the absolute value is multiplied by a negative sign.
Based on this information, the equation of the graph should be of the form:
Thus, the correct equation from the provided options is:
This corresponds to the option on the far left: .
Would you like further details or explanations?
Here are 5 related questions:
- How do you determine the vertex of an absolute value function from its graph?
- What causes an absolute value graph to open downward instead of upward?
- How does a vertical shift affect the equation of an absolute value function?
- What is the general form of an absolute value function?
- How would you describe horizontal shifts in the equation of an absolute value function?
Tip: When analyzing absolute value graphs, always check for shifts (horizontal or vertical) and whether the graph opens upward or downward.
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Math Problem Analysis
Mathematical Concepts
Absolute Value Functions
Graph Transformations
Formulas
f(x) = a|x - h| + k
Theorems
Basic properties of absolute value functions
Suitable Grade Level
Grades 9-12
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