How do you graph y=-4cos(1/2x-pi)+3?

1 Answer
Feb 12, 2018

There are four main components in graphing this function:

Explanation:

  • Amplitude - twice the y distance from maximum to minimum
  • Period - the x distance between a repetition of the values
  • Horizontal Phase Shift - the shift on the x axis
  • Vertical Phase Shift - the shift on the y axis

In the function a*cos(bx+c)+d

  • Amplitude = a
  • Period = (2pi)/b
  • Horizontal Phase Shift = c/b
  • Vertical Phase Shift = d

Thus you can figure out:

  • Amplitude = 4
  • Period = pi
  • Horizontal Phase Shift = -pi/2
  • Vertical Phase Shift = 3

Note:

The amplitude is always positive because distances can not be negative. When the a term is negative there is a flip over the x axis

When you graph this function you will get:
graph{-4*cos(1/2x-pi)+3 [-9.46, 10.54, -1.76, 8.24]}