Question

The x-axis ranges from Start Fraction negative 4 pi over 5 End Fraction to Start Fraction 8 pi over 5 End Fraction in increments of Start Fraction 2 pi over 5 End Fraction. The y-axis ranges from negative 2 to 6 in increments of 1. The waveform passes through coordinates left parenthesis Start Fraction negative 4 pi over 5 End Fraction comma 2 right parenthesis, left parenthesis Start Fraction negative 3 pi over 5 End Fraction comma 5 right parenthesis, left parenthesis Start Fraction negative 2 pi over 5 End Fraction comma 2 right parenthesis, left parenthesis Start Fraction negative pi over 5 End Fraction comma negative 1 right parenthesis, left parenthesis 0 comma 2 right parenthesis, left parenthesis Start Fraction pi over 5 End Fraction comma 5 right parenthesis, left parenthesis Start Fraction 2 pi over 5 End Fraction comma 2 right parenthesis, left parenthesis Start Fraction 3 pi over 5 End Fraction comma negative 1 right parenthesis, left parenthesis Start Fraction 4 pi over 5 End Fraction comma 2 right parenthesis, left parenthesis pi comma 5 right parenthesis, left parenthesis Start Fraction 6 pi over 5 End Fraction comma 2 right parenthesis, left parenthesis 7 pi over 5 End Fraction comma negative 1 right parenthesis, and left parenthesis Start Fraction 8 pi over 5 End Fraction comma 2 right parenthesis.

Which function is shown on the graph?

(1 point)

f(x)=3sin(5x2)+2


f(x)=3sin(5x2)−2


f(x)=3sin(x2)+2


f(x)=5sin(5x2)+2

Skip to navigation

Answer 1

f(x) = 3 sin(5x/2) + 2

Reason: midline is 2 and amplitude 3 (y ranges 2±3). Peaks repeat every 4π/5, so period T = 4π/5 gives angular frequency k = 2π/T = 5/2. Thus f(x)=3 sin((5/2)x)+2 (option 1).