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

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 $a \cdot \cos \left(b x + c\right) + d$

• Amplitude = $a$
• Period = $\frac{2 \pi}{b}$
• Horizontal Phase Shift = $\frac{c}{b}$
• Vertical Phase Shift = $d$

Thus you can figure out:

• Amplitude = $4$
• Period = $\pi$
• Horizontal Phase Shift = $- \frac{\pi}{2}$
• 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]}