Math Problem Statement
Solution
To determine the transformation that converts the graph of into the graph of , we can break it down step by step:
Step 1: Analyze Vertical Transformation
- In , the coefficient of the absolute value is .
- In , the coefficient of the absolute value is .
- This change from to represents a vertical shrink because the magnitude of the coefficient decreases (making the graph less steep).
Step 2: Analyze Horizontal Transformation
- In , the horizontal shift is , indicating a shift 2 units to the right.
- In , the horizontal shift is , indicating a shift 4 units to the right.
- This shows a horizontal shift of 2 units further to the right, but that doesn't affect the question choices.
Step 3: Conclusion
The primary transformation between the two functions is the change in the vertical scaling from to , which is a vertical shrink.
Thus, the correct answer is vertical shrink.
Would you like further details or have any additional questions?
Related Questions:
- What would a horizontal stretch look like in this context?
- How does a vertical reflection affect the graph of a function?
- Can you explain how shifting impacts the domain of absolute value functions?
- What would happen if we changed the constant outside the absolute value expression?
- How do horizontal shifts differ from horizontal stretches in terms of function transformation?
Tip:
When the coefficient inside the absolute value changes, it affects horizontal transformations, while changes outside affect vertical transformations.
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Math Problem Analysis
Mathematical Concepts
Transformations
Absolute Value Functions
Formulas
y = a|x - h| + k
Theorems
Transformation properties of functions
Suitable Grade Level
Grades 9-12
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