To show the order of operations that transforms the function \( f(x) = x^2 \) to \( f(-2x) + 3 \), we can create a table that highlights each transformation step-by-step.
Table of Transformations
| Step | Transformation | Result | |------|----------------------|-----------------------------| | 1 | Start with | \( f(x) = x^2 \) | | 2 | Substitute \( -2x \) | \( f(-2x) = (-2x)^2 = 4x^2 \)| | 3 | Add 3 | \( f(-2x) + 3 = 4x^2 + 3 \) |
Summary of Steps
- Start with the original function \( f(x) = x^2 \).
- Substitute \( -2x \) into the function, which results in \( f(-2x) = (-2x)^2 = 4x^2 \).
- Finally, add 3 to the result of step 2 to obtain \( f(-2x) + 3 = 4x^2 + 3 \).
This table helps illustrate the steps involved in transforming \( f(x) = x^2 \) into \( f(-2x) + 3 \).