Math Problem Statement
which equation represents the graph of y=f(x) after it is reflected in the y axis then translated horizontally 2 units to the left?
Solution
To transform the graph of based on the given transformations:
Step 1: Reflect in the y-axis
Reflection across the y-axis replaces with . The equation becomes:
Step 2: Translate 2 units to the left
Translation 2 units to the left replaces with . Applying this to , the new equation becomes:
Final Equation:
This is the equation that represents the graph of after reflecting it across the y-axis and translating it 2 units to the left.
Do you want more details on any part of the transformations?
Here are 5 related questions you might find interesting:
- How do reflections across the x-axis differ from reflections across the y-axis in terms of equations?
- What is the effect of horizontal translations on the graph of ?
- How can multiple transformations be applied in different orders?
- What changes would occur if the graph were translated 2 units to the right instead?
- How can the transformations be visualized step-by-step using a graph?
Tip: Always apply transformations in the correct sequence (e.g., reflections before translations) to avoid errors.
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Math Problem Analysis
Mathematical Concepts
Transformations of functions
Reflections
Translations
Formulas
y = f(-x)
y = f(-(x + h)) for horizontal translations after reflection
Theorems
Transformation rules for functions
Suitable Grade Level
Grades 9-12
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