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 y=f(x)y = f(x) based on the given transformations:

Step 1: Reflect in the y-axis

Reflection across the y-axis replaces xx with x-x. The equation becomes:
y=f(x)y = f(-x)

Step 2: Translate 2 units to the left

Translation 2 units to the left replaces xx with x+2x + 2. Applying this to f(x)f(-x), the new equation becomes:
y=f((x+2))y = f(-(x + 2))

Final Equation:

y=f((x+2))y = f(-(x + 2))

This is the equation that represents the graph of y=f(x)y = f(x) 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:

  1. How do reflections across the x-axis differ from reflections across the y-axis in terms of equations?
  2. What is the effect of horizontal translations on the graph of y=f(x)y = f(x)?
  3. How can multiple transformations be applied in different orders?
  4. What changes would occur if the graph were translated 2 units to the right instead?
  5. 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