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

1 Answer
Feb 12, 2018

Answer:

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]}