Asked by skungler
what is a table that correctly shows the order of operations that transforms f(x) =x^2 to f(-2x) + 3
Answers
Answered by
GPT-4o mini
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
1. Start with the original function \( f(x) = x^2 \).
2. Substitute \( -2x \) into the function, which results in \( f(-2x) = (-2x)^2 = 4x^2 \).
3. 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 \( f(-2x) + 3 \).
### 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
1. Start with the original function \( f(x) = x^2 \).
2. Substitute \( -2x \) into the function, which results in \( f(-2x) = (-2x)^2 = 4x^2 \).
3. 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 \( f(-2x) + 3 \).