Question

Use the image to answer the question.

Five labeled sinusoidal waves are plotted on a coordinate plane.
▶Click for Long Desc

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

(1 point)

Option 2 is the graph of −f(x)
.

Option 2 is the graph of f(−x)
.

Option 2 is the graph of f(x−7)
.

Option 2 is the graph of −f(−x)
.
Skip to navigation

Answer 1

I don't have the image visible — could you describe how Option 2 differs from f(x)=sin x + 2? Useful details:

- Is the midline at y = 2, y = −2, or somewhere else?
- Are peaks where they normally are for sin x (e.g. at x = π/2 + 2πk) or are they shifted horizontally?
- Are peaks turned into troughs (i.e. reflected across the x-axis)?

To help you match it right away, here is what each algebraic option does to f(x)=sin x + 2:

- −f(x) = −sin x − 2: reflected across the x-axis (peaks become troughs) and midline goes to y = −2.
- f(−x) = sin(−x) + 2 = −sin x + 2: reflected across the y-axis (horizontal mirror), midline stays at y = 2, peaks become troughs.
- f(x−7) = sin(x−7) + 2: shifted right 7 units, midline stays at y = 2, shape/orientation unchanged.
- −f(−x) = −(sin(−x) + 2) = sin x − 2: midline goes to y = −2, orientation is the same as the original (peaks stay peaks).

Tell me which of those descriptions matches Option 2 (midline and whether peaks are inverted or shifted), and I’ll give the correct choice.