Question

Use the image to answer the question.

A waveform is graphed on a coordinate plane. The x-axis ranges from negative pi to Start Fraction 5 pi over 2 End Fraction in increments of Start Fraction pi over 2 End Fraction. The y-axis ranges from negative 1 to 3 in increments of 1.

Determine which function matches the given graph.

A). f (x) = -sin (2 (x-π/4))+1
B). f (x) = -sin (1/2 (x-π/4))+1
C). f (x) = -sin (2 (x+π/4))+1
D). f (x)= sin (2 (x-π/4))+1

Answer 1

A

Reason: The graph has amplitude 1 and midline y = 1, so candidate forms are ±sin(2x + phase) + 1 (period π). Option B has period 4π so is impossible. Options C and D both simplify to -cos(2x)+1, which has maxima at x = π/2 + kπ, but the graph's maxima occur at x = kπ (including x = 0). Option A simplifies to cos(2x)+1, which has maxima at x = kπ, matching the plotted maxima, so A is correct.