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Five labeled sinusoidal waves are plotted on a coordinate plane.

Describe the transformation of the graph of f(x)=sinx+2
to the graph labeled Option 2.

(1 point)
Responses

Option 2 is the graph of f(x−7)
.
Option 2 is the graph of f of open paren x minus 7 close paren.

Option 2 is the graph of −f(−x)
.
Option 2 is the graph of negative f times negative x.

Option 2 is the graph of −f(x)
.
Option 2 is the graph of negative f times x.

Option 2 is the graph of f(−x)
.

1 answer

To describe the transformation of the graph of \( f(x) = \sin x + 2 \) to the graph labeled as Option 2, we need to analyze the properties of the sine function and any transformations applied to it.

  1. The function \( f(x) = \sin x + 2 \) represents a vertical shift of the standard sine wave \( \sin x \) upward by 2 units.

Now, without seeing the graph, we can make educated guesses about potential transformations based on the listed options.

  • Option 1: \( f(x-7) \) - This is a horizontal shift of the graph to the right by 7 units. This does not match the transformation described.

  • Option 2: \( f(x - 7) \) - Same as Option 1, would not match the transformation described.

  • Option 3: \( -f(-x) \) - This represents a reflection across both axes. It reflects the graph upside down and flips it horizontally, which is a more complex transformation.

  • Option 4: \( -f(-x) \) - Same interpretation as Option 3, also complex, so it’s unlikely to match.

  • Option 5: \( -f(x) \) - This represents reflection of the graph across the x-axis.

  • Option 6: \( f(-x) \) - This is a horizontal reflection across the y-axis.

To summarize, if Option 2 corresponds to a transformation from the original graph, it may involve some form of reflection or shifting. If the graph is not just shifted upward but altered through reflection, we would see changes consistent with options involving negations.

Given these analyses, there’s not enough specification to select a particular option without seeing what the transformation looks like. However, if Option 2 reflects the sine function downwards while shifting it, then it could be consistent with \( -f(x) \).

If you can deduce that Option 2 indicates a reflection, the option that would best describe the transformation from the original graph to Option 2 would likely be:

Option 5: Option 2 is the graph of \( -f(x) \).

However, if the transformation resulted in a horizontal shift or some other specific transformation not involving reflection, please refer back to the graphical representation to make the most accurate selection.