Final answer:
To graph the inequality x² + (y - 1)² ≤ 1, start by sketching the graph of the equation x² + (y - 1)² = 1. Then, determine the inequality symbol to see if you should shade in the region inside the circle or just the circle itself.
Step-by-step explanation:
To graph the inequality x² + (y - 1)² ≤ 1, we can start by sketching the graph of the equation x² + (y - 1)² = 1, which represents the boundary of the inequality. This equation represents a circle with center (0, 1) and radius 1. Plot the center point (0, 1) and then mark points around the circle, such as (1, 1), (-1, 1), (0, 2), and (0, 0).
Next, determine whether the inequality is less than or equal to, or just less than. Since the inequality states ≤, we need to include the points on the boundary of the circle as well. Shade in the region inside the circle and on the boundary.
Now, we have successfully graphed the inequality x² + (y - 1)² ≤ 1. The shaded region represents all the points that satisfy this inequality.