Final answer:
The graph of the inequality W < 115x^2 is a parabola opening upwards with the region below it, not including the boundary, representing safe weight capacities based on the shelf's thickness.
Step-by-step explanation:
The inequality that represents the weight W (in pounds) that a hardwood shelf can safely support based on its thickness x (in inches) is given by W < 115x^2. To graph this inequality, you would plot W on the vertical axis and x on the horizontal axis. The region below the parabola defined by W = 115x^2 represents all the combinations of x and W that satisfy the inequality, meaning that for each thickness x, the shelf can safely support any weight less than 115x^2 pounds. The boundary of this region, the parabola itself, is typically drawn as a dashed line to indicate that points on the line are not included in the solution set for the inequality (since the question specifies '<' rather than '≤').