Math Problem Statement
The graph of β is obtained when π(π₯) =β 3π₯ is reflected along the 2 + 12 line π¦ = 0. Write down the equation of β in the form β(π₯) = ππ₯ 2 + π.
Solution
Let's break down the problem step-by-step:
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Given Function: We start with .
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Reflection Line: The reflection line is , which is the x-axis.
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Reflection of Along the x-axis:
- When we reflect across the x-axis, we change the sign of .
- The reflection of across is .
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Writing in the Given Form:
- We want in the form .
- Since is a linear function, and simplifies to a constant term, .
Final Answer: [ h(x) = 3x
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Math Problem Analysis
Mathematical Concepts
Algebra
Reflections
Linear Functions
Formulas
Reflection of a function: y = -f(x) when reflected across the x-axis
Theorems
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Suitable Grade Level
Grades 9-10