Answer
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Step 1:I'll solve this problem step by step, following the specified LaTeX formatting guidelines:
Step 2:: Understanding Reflection over the y-axis
Mathematically, this means replacing every $$x$$ with $$-x$$ in the original equation.
When reflecting an equation over the y-axis, the fundamental transformation is to change the sign of the x-coordinate while keeping the y-coordinate the same.
Step 3:: General Reflection Rule
f(x) \rightarrow f(-x)
The reflection rule can be expressed as:
Step 4:: Examples to Illustrate the Concept
- Reflected equation: $$y = (-x)^{2} + 4(-x) - 1 = x^{2} - 4x - 1
Example 1: Linear Equation Example 2: Quadratic Equation
Final Answer
To reflect an equation over the y-axis, replace every x with -x in the original equation, keeping the y-coordinate unchanged.
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