Question

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

1. Find the amplitude of the function. State the range of the function.

2. Find the period of the function. Find the key points of the function [intercept(s), maximum(s), and minimum(s)] for 1 period. Show all work.

3. Sketch the graph of g (one period), alongside the graph of f(x) = sinx on the interval [0,2/pi]. Label the axes.

For problems 4, 5, and 6, use the function g(x)=cos((x)/(4)).

4. Find the amplitude of the function. State the range of the function.

5. Find the period of the function. Find the key points of the function [intercept(s), maximum(s), and minimum(s)] for 1 period. Show all work.

6. Sketch the graph of g, alongside the graph of f(x) = cosx on the interval [0,2/pi] . Label the axes.

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)  $\left( \frac{\pi}{4}, \, -1 \right)$