Math Problem Statement
y=√x-6
Solution
The equation you've provided is:
This describes a transformation of the square root function . Here's how:
- Parent Function: The base function is , which starts at the point and gradually increases as increases.
- Vertical Shift: The entire graph of is shifted 6 units downwards because of the subtraction of 6.
Key Points:
- Domain: Since is only defined for non-negative , the domain is .
- Range: Since the square root of any number is non-negative and the graph is shifted down by 6, the range is .
If you want to sketch the graph, it would start at the point and gradually rise as increases.
Would you like more details or have any questions?
Related Questions:
- How do we find the inverse of ?
- What are the intercepts of the graph of ?
- How does the function behave as ?
- Can we express the equation in terms of a piecewise function?
- How can we apply transformations to the graph ?
Tip: The square root function is non-linear, so shifts impact the graph differently than for linear functions like .
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Math Problem Analysis
Mathematical Concepts
Algebra
Square Root Function
Function Transformations
Formulas
y = √x
y = √x - 6
Theorems
Function Transformation Theorem
Suitable Grade Level
Grades 9-10
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