Final answer:
To graph the inequality x - y² < 4, plot the parabola x = y² + 4 using a dashed line and then shade the region to the left of this curve that satisfies the inequality.
Step-by-step explanation:
Graphing the inequality x - y² < 4 involves determining the region in the xy-plane that satisfies the condition laid out by the inequality. The border of this region is the parabola defined by the equation x = y² + 4. To graph this inequality, we first plot the parabola by calculating a few (x, y) pairs based on the equation, and then sketch the curve. Since it is a 'less than' inequality and not 'less than or equal to', we will use a dashed line to indicate that points on the line are not included in the solution set. The next step is to identify the region that satisfies the inequality, which is the area where the values of x are less than y² + 4. We select a test point, such as (0, 0), plug it into the inequality, and if it satisfies the inequality, which it does in this case, we shade the area that includes that point. This falls to the left of the sketched parabola when we are looking at the graph.