Math Problem Statement
Solution
The problem asks for the equation of the blue graph , which is stated to have the same shape as the red graph . This implies that is a transformation of , specifically a horizontal shift, since the two graphs appear identical except for their position along the x-axis.
Analysis:
- The red graph passes through the origin, whereas the blue graph seems to have the same shape but is shifted left.
- A horizontal shift of a cubic function can be described by , where is the shift. From the graph, it appears the blue graph is shifted 3 units to the left, which gives the equation:
Conclusion:
The equation of the blue graph is , which corresponds to option C.
Let me know if you want more details or have any questions! Here are five follow-up questions related to this topic:
- How does a horizontal shift affect the graph of a function?
- What is the difference between horizontal and vertical shifts in transformations?
- How can you identify a vertical shift from a graph?
- What happens to the graph of when you apply a reflection over the y-axis?
- Can you describe how other types of transformations (like stretching or compressing) would modify the graph of ?
Tip: When analyzing graph transformations, always look at the vertex (or the key point) and check if the movement is horizontal, vertical, or both.
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Math Problem Analysis
Mathematical Concepts
Algebra
Graph Transformations
Cubic Functions
Formulas
Horizontal shift: G(x) = (x + h)^3
Theorems
Function Transformation Theorem
Suitable Grade Level
Grades 9-11