Question

The waveform passes through coordinates left parenthesis negative pi comma 2 right parenthesis, left parenthesis Start Fraction negative pi over 2 End Fraction comma 0 right parenthesis, left parenthesis 0 comma 2 right parenthesis, left parenthesis Start Fraction pi over 2 End Fraction comma 0 right parenthesis, left parenthesis pi comma 2 right parenthesis, left parenthesis Start Fraction 3 pi over 2 End Fraction comma 0 right parenthesis, left parenthesis 2 pi comma 2 right parenthesis, and left parenthesis Start Fraction 5 pi over 2 End Fraction comma 0 right parenthesis.

Determine which function matches the given graph.

(1 point)

f(x)=−sin(2(x−π4))+1


f(x)=sin(2(x−π4))+1


f(x)=−sin(12(x−π4))+1


f(x)=−sin(2(x+π4))+1

Answer 1

f(x) = −sin(2(x − π/4)) + 1

Reason: The graph has max 2 and min 0 so midline 1 and amplitude 1. The horizontal repeat is π so B = 2. Plugging x = 0 gives −sin(2(0 − π/4)) + 1 = −sin(−π/2) + 1 = 2, and the function then matches the other given points, so option 1 is correct.