Math Problem Statement
Answer
Solution
We are given that:
- The domain of is
- The range of is
We need to find the domain and range of the function .
1. Finding the Domain of :
The transformation represents a horizontal shift of the function to the right by 6 units.
- If the domain of is , after shifting the graph to the right by 6 units, the new domain will be shifted accordingly.
- Therefore, the domain of is .
2. Finding the Range of :
A horizontal shift does not affect the range of the function. Therefore, the range of remains the same as the range of .
- The range of is still .
Final Answer:
- Domain of :
- Range of :
Would you like more details or clarifications?
Related Questions:
- What happens to the domain when shifting the graph left by 4 units?
- How would the range change if we applied a vertical shift instead?
- What transformation would cause the range to change but not the domain?
- How do we handle vertical stretches or compressions when determining range?
- Can you find the inverse of the function and determine its domain and range?
Tip: When a function is shifted horizontally, the domain changes, but the range remains unaffected.
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Math Problem Analysis
Mathematical Concepts
Functions
Transformations
Domain
Range
Formulas
-
Theorems
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Suitable Grade Level
Grades 9-12
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