Math Problem Statement
Use transformations to graph the given function a(x) = √(2x).
Solution
The problem involves graphing the function using transformations.
Explanation:
- The base function is , which is the square root function.
- The transformation involves multiplying by a factor of 2 inside the square root, resulting in a horizontal compression of the graph by a factor of . This means the graph becomes "narrower" as the -values are effectively scaled down.
- Domain: Since you cannot take the square root of a negative number, the domain of is .
Observations:
- The graph starts at the origin , as .
- It increases smoothly for positive -values.
Let me know if you'd like a step-by-step breakdown or need anything else explained.
Follow-up Questions:
- What are the differences between horizontal and vertical transformations?
- How does scaling inside the square root differ from scaling outside it?
- Can you determine the range of ?
- How would the graph look if the function were ?
- How does the transformation affect the slope of the graph at different points?
Tip:
When working with transformations, always identify how the coefficient affects the -values (inside functions) or -values (outside functions).
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Math Problem Analysis
Mathematical Concepts
Graph transformations
Square root functions
Formulas
a(x) = √(2x)
Theorems
-
Suitable Grade Level
Grades 9-11
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