# How do you determine the amplitude, period, and shifts to graph #f(x)= 10 cos 3x#?

##### 1 Answer

Amplitude

Period

Phase Shift

Vertical Shift

#### Explanation:

The general equation for a cosine function is:

#f(x)=acos(k(x-d))+c#

The amplitude is the peak height subtract the trough height divided by

Additionally, the amplitude is also the absolute value found before

#Amplitude=|a|#

The period is the length from one point to the next matching point. It can also be described as the change in the independent variable (

Additionally, the period is also

#Period=360^@/|k|# or#Period=(2pi)/|k|#

The phase shift is the length that the transformed graph has shifted horizontally to the left or right compared to its parent function. In this case,

The vertical shift is the length that the transformed graph has shifted vertically up or down compared to its parent function.

Additionally, the vertical shift is also the maximum height plus the minimum height divided by

#"Vertical shift"=("maximum y"+"minimum y")/2#