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What are the important points to graph #y=sin(3x-pi/3)#?

Answer 1

Zoe Austin

As below.

Standard form of a sine function is #y = A sin (Bx - C) + D#

#"Given " y = sin (3x - pi/3)#

#A = 1, B = 3, C = pi/3, D = 0#

Important points to graph are Amplitude, Period, Phase Shift and Vertical Shift.

#Amplitude = |A| = 1#

#"Period ' = (2pi) / |B| = (2pi) / 3#

#"Phase Shift " = -C / B = -9pi/3) / 3 = -pi/9, color(red)((pi/9) " to the LEFT"#

#"Vertical Shift " = D = 0#

graph{sin (3x - pi/3) [-10, 10, -5, 5]}

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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