Question

For problems 1, 2, and 3, use the function g(x) = sin(6x) .

Answer 1

Step-by-step explanation:

1. Amplitude = 1.  g(x) = 1 sin(6x).  The coefficient 1 is the amplitude.  The range of the function is $-1 \le g(x) \le 1$  or, in interval notation, [-1, 1]

2. The period is  $\frac{2\pi}{6}=\frac{\pi}{3}$.

x-intercepts (at the beginning, middle, and end of the period) $0,\,\frac{\pi}{6},\,\frac{\pi}{3}$

Maximum (1/4 of way through period)  $\left(\frac{\pi}{12},\,1 \right)$

Minimum (3/4 of way through period)  $\left( \frac{\pi}{4}, \, -1 \right)$