Use the image to answer the question.

Five labeled sinusoidal waves are plotted on a coordinate plane.

Describe the transformation of the graph of f(x) to the graph labeled Option 3.

(1 point)
Responses

Option 3 is the graph of f(−x).
Option 3 is the graph of f left parenthesis negative x right parenthesis .

Option 3 is the graph of −f(x).
Option 3 is the graph of f left parenthesis negative x right parenthesis .

Option 3 is the graph of f(x)+1.
Option 3 is the graph of f left parenthesis negative x right parenthesis .

Option 3 is the graph of −f(−x).
Option 3 is the graph of f left parenthesis negative x right parenthesis .
Skip to navigation

1 answer

To determine the transformation from the graph of \( f(x) \) to the graph labeled Option 3, let's review the possible transformations associated with the functions provided:

  1. Option \( f(-x) \): This indicates a reflection across the y-axis.
  2. Option \(-f(x)\): This indicates a reflection across the x-axis.
  3. Option \( f(x) + 1 \): This indicates a vertical shift upward by 1 unit.
  4. Option \(-f(-x)\): This indicates a reflection across the y-axis followed by a reflection across the x-axis, which results in a reflection across the origin.

Given the options listed, if Option 3 appears to reflect the original graph across the y-axis, then the correct transformation would be \( f(-x) \). If it reflects across the x-axis, then it would be \(-f(x)\). If it does a combination of both transformations, it would correspond to \(-f(-x)\).

Since the question asks to describe the transformation leading to the specific graph labeled as Option 3, you need to identify which transformation matches the characteristics of the graph in question.

If you can provide any visual details or specific descriptions of Option 3's graph in comparison to \( f(x) \), then I could narrow down the appropriate selection. Based on your input, I can conclude which response best fits the transformation to Option 3.