Question

The horizontal axis ranges from start fraction negative pi over 4 end fraction to start fraction 3 pi over 4 end fraction in increments of start fraction pi over 4 end fraction. The vertical axis ranges from negative 1 to 1 in increments of 1. The waveform peaks at y equals 1 and valleys at y equals negative 1. The curve begins at left parenthesis start fraction negative pi over 4 end fraction comma 0 right parenthesis and continues through left parenthesis start fraction negative pi over 8 end fraction comma negative 1 right parenthesis, left parenthesis 0 comma 0 right parenthesis, left parenthesis start fraction pi over 8 end fraction comma 1 right parenthesis, left parenthesis start fraction pi over 4 end fraction comma 0 right parenthesis, left parenthesis start fraction 3 pi over 8 end fraction comma negative 1 right parenthesis, left parenthesis start fraction pi over 2 end fraction comma 0 right parenthesis, left parenthesis start fraction 5 pi over 8 end fraction comma 1 right parenthesis. The curve ends at left parenthesis start fraction 3 pi over 4 end fraction comma 0 right parenthesis.

Identify the function in the graph.

(1 point)
Responses

f(x)=sin(4x)

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

f(x)=cos(4x)

f left parenthesis x right parenthesis equals cosine left parenthesis 4 x right parenthesis
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Answer 1

f(x) = sin(4x)

Reason: zeros are spaced by π/4, so the angular frequency is 4 (spacing = π/k → k=4). Check points: sin(4·(−π/8)) = sin(−π/2) = −1, sin(4·π/8) = sin(π/2) = 1, etc., matching the graph.