Answered

Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Experience the convenience of getting reliable answers to your questions from a vast network of knowledgeable experts. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

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.

Sagot :

ivycoveredwalls

Step-by-step explanation:

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

2. The period is  [tex]\frac{2\pi}{6}=\frac{\pi}{3}[/tex].

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

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

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

View image ivycoveredwalls
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.