Question

Question
Use the image to answer the question.

A waveform is plotted on a coordinate plane.
▶Click for Long Desc

Identify the function in the graph.

(1 point)
Responses

f(x)=cos(4x)

f left parenthesis x right parenthesis equals cosine left parenthesis 4 x right parenthesis

f(x)=sin(2x)

f left parenthesis x right parenthesis equals sine left parenthesis 2 x right parenthesis

f(x)=sin(4x)

f left parenthesis x right parenthesis equals sine left parenthesis 4 x right parenthesis

f(x)=sin(−4x)

Answer 1

I can't see the image you referenced. Could you either attach the picture or give a short description of the graph (value at x=0, where peaks and zeros occur, distance between consecutive peaks or zeros)?

If you want to check it yourself, here's the quick method to identify which of the four choices fits:

1. Check f(0):
- If f(0)=1 (maximum) it’s cosine-like (cos(4x) if frequency matches).
- If f(0)=0 it’s sine-like (some multiple of sin).
2. Find the period T (distance between two consecutive peaks or two consecutive zeros with same direction).
- B in sin(Bx) or cos(Bx) equals 2π/T. So T = 2π/B.
- For sin(2x): T = π (one full cycle every π).
- For sin(4x) or cos(4x): T = π/2 (one full cycle every π/2).
3. Check the slope at x=0 (or just the sign of the first quarter after 0):
- If graph passes through 0 and is increasing at 0 → positive sine (sin(4x) if period matches).
- If it passes through 0 and is decreasing at 0 → negative sine (sin(−4x) = −sin(4x)).
- If it starts at a maximum at 0 (and then decreases) → cos(4x) if period matches.

Tell me the value at x=0 and the horizontal distance between two successive peaks (or zeros) and I’ll pick the exact choice.