Given the function f (x) = 3cos x for the interval 0 < x < 2 sketch the graph of the function

http://www.wolframalpha.com/input/?i=plot+3cos+x+%2C+0+≤+x+≤+2

To sketch the graph of the function f(x) = 3cos(x) for the interval 0 < x < 2, you can follow these steps:

Step 1: Determine the key points and shape of the graph
- The function f(x) = 3cos(x) is a cosine function, which has a periodic nature.
- The amplitude of the cosine function is 3, which determines the vertical range of the graph.
- The period of the cosine function is 2π, which means the pattern repeats every 2π units along the x-axis.
- The graph of the cosine function starts at the maximum value and then oscillates between the maximum and minimum values.

Step 2: Determine the x-axis values for the interval 0 < x < 2
- Since the interval is 0 < x < 2, you need to find the x-axis values that fall within this range. In this case, the range is from 0 to 2.
- You can choose a few specific x-axis values such as x = 0, 1/2, 1, 3/2, and 2.

Step 3: Calculate the corresponding y-axis values
- Plug in the chosen x-axis values into the function f(x) = 3cos(x) to find the corresponding y-axis values.
- For example, when x = 0, f(0) = 3cos(0) = 3. So, you have the point (0, 3).
- Similarly, when x = 1/2, f(1/2) = 3cos(1/2) ≈ 2.598. So, you have the point (1/2, 2.598).

Step 4: Plot the points and sketch the graph
- Now, plot the points you calculated in step 3 on a set of coordinate axes.
- Connect the points smoothly, maintaining the shape of a cosine function.
- Note that since the interval is 0 < x < 2, the graph should not extend beyond these limits.

Following these steps, you can sketch the graph of the function f(x) = 3cos(x) for the interval 0 < x < 2.