Draw the graph of y = cos⁻¹(x), where ⋅ represents the fractional part function.

To graph the function \( y = \cos^{-1}(x) \), we first need to understand its characteristics. The inverse cosine function, also known as arccosine, takes an input \( x \) in the range of \([-1, 1]\) and outputs an angle \( y \) in the range of \([0, \pi]\).

Key Features of the Graph

• Domain: The function is defined for \( x \) values between -1 and 1.
• Range: The output values (angles) range from 0 to \( \pi \) radians (approximately 3.14).
• Shape: The graph is a decreasing curve, starting from the point (-1, \( \pi \)) and ending at (1, 0).

Steps to Draw the Graph

1. Start by plotting the points at the endpoints: (-1, \( \pi \)) and (1, 0).
2. Identify key points in between, such as (0, \( \frac{\pi}{2} \)).
3. Draw a smooth curve connecting these points, ensuring it decreases from left to right.

Graph Representation

The graph will look like a downward-sloping curve starting from the top left and moving to the bottom right, reflecting the nature of the inverse cosine function. Remember, the graph will not extend beyond the specified domain and range.

By following these steps, you can create an accurate representation of the function \( y = \cos^{-1}(x) \).