identify the amplitude and period of the graph of the function. the amplitude is and the period is.
identify the amplitude and period of the graph of the function. the amplitude is and the period is.
Answer
Explanation:
Step1: Define amplitude
Amplitude is the distance from the mid - line to the maximum or minimum. The maximum value of the function is 4 and the minimum is - 4. The mid - line is $y = 0$. So, amplitude $A=\frac{\text{max}-\text{min}}{2}$. $A=\frac{4 - (-4)}{2}=\frac{8}{2}=4$
Step2: Define period
The period is the horizontal distance between two consecutive points with the same value and slope. The graph repeats itself from $x = 0$ to $x=6\pi$. So, the period $T = 6\pi$.
Answer:
The amplitude is 4 and the period is $6\pi$.