To determine the transformation of the graph of \( f(x) = 2x \) to the graph labeled Option 3, we need to look for the specific transformations that are applied.
- Translation: Shifts the graph left or right.
- Reflection: Flips the graph over the x-axis or y-axis.
- Vertical Stretch/Compression: Changes the scale of the graph vertically.
Given your provided options, let's analyze them briefly:
- \( f(x - 1) \): This represents a horizontal shift to the right by 1 unit.
- \( -f(x) \): This reflects the graph over the x-axis.
- \( f(-x) \): This reflects the graph over the y-axis.
- \( -f(-x) \): This reflects the graph over both axes and then scales it vertically.
Without the image, I can't directly identify the transformation, but I can explain how to choose the right response based on what you see.
For example:
- If Option 3 looks like a reflection of \( f(x) \) across the x-axis, then the correct answer would be \( -f(x) \).
- If it looks like a horizontal reflection, the answer would be \( f(-x) \).
- If it appears to be shifted left or right, look for \( f(x - 1) \) or \( f(x + 1) \).
You would select the option based on the specific transformation observed in Option 3 compared to the original graph of \( f(x) = 2x \).
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