Question

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

Answer 1

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]}