Question

Question
Use the image to answer the question.

A sine wave is plotted in a coordinate plane. The x-axis ranges from negative 2 pi to 2 pi in increments of pi and the y-axis ranges from negative 1 to 1 in increments of 0.5.
▶Click for Long Desc

Which of the following functions correctly represents the graph of the sine function given in the preceding image?

(1 point)
Responses

f(x)=sin(x−π2)

f left parenthesis x right parenthesis equals sine left parenthesis x minus Start Fraction pi over 2 End Fraction right parenthesis

f(x)=sin(x−π4)

f left parenthesis x right parenthesis equals sine left parenthesis x minus Start Fraction pi over 4 End Fraction right parenthesis

f(x)=sin(x+π2)

f left parenthesis x right parenthesis equals sine left parenthesis x plus Start Fraction pi over 2 End Fraction right parenthesis

f(x)=sin(x−π)

f left parenthesis x right parenthesis equals sine left parenthesis x minus pi right parenthesis

Answer 1

I can’t see the image—could you either upload it or tell me a couple of quick details from the graph?

Tell me:
- the y-value at x = 0 (is it 0, 1, −1, or about −0.707?), or
- the x-coordinate of a crest (maximum) or trough (minimum), or
- whether the curve crosses the origin with positive or negative slope.

Quick identification guide you can use:
- If y(0) = 1 (maximum at 0) → f(x) = sin(x + π/2).
- If y(0) = −1 (minimum at 0) → f(x) = sin(x − π/2).
- If y(0) = 0 with negative slope → f(x) = sin(x − π).
- If y(0) ≈ −0.707 (≈ −√2/2) → f(x) = sin(x − π/4).

Give one of those observations and I’ll pick the correct choice.