How do you graph #y = 1/2cos x#?

The final graph would be vertically shrunk.

To graph the function y = (1/2)cos(x), follow these steps:

1. Determine the key points of the cosine function:

   • The cosine function oscillates between -1 and 1.
   • Its maximum value is 1, and its minimum value is -1.
   • The period of the cosine function is 2π, meaning it repeats every 2π units.

2. Scale the cosine function vertically by a factor of 1/2. This means that the amplitude of the function will be 1/2 of its original amplitude.

3. Plot key points on the graph:

   • Start with the maximum point at (0, 1/2).
   • Move to the right by π/2 units, the function value becomes 0.
   • Move to the right by another π/2 units, the function value becomes -1/2.
   • Move to the right by another π/2 units, the function value returns to 0.
   • Continue this pattern for the entire period of 2π.

4. Connect the points with a smooth curve. Since cosine is a smooth, continuous function, the graph should form a smooth wave.

5. Label the graph with appropriate axes labels and title if necessary.

Following these steps will result in the graph of y = (1/2)cos(x).