Question

Two different businesses model their profits over 15 years. The function f(x) represents the profit of the garden shop and g(x) represents the profit of the construction material business. What is the relationship between f(x) and g(x)?

Answer 1

The profit functions f(x) and g(x) have an inverse relationship, where an increase in one business's profit leads to a decrease in the other business's profit.

Step-by-step explanation:

The relationship between the profit functions f(x) and g(x) can be determined by analyzing their behavior over the 15-year period. Since the question states that the product of f(x) multiplied by g(x) equals a constant, we can infer that the two businesses have an inverse relationship. This means that when one business's profit increases, the other business's profit decreases, and vice versa. For example, if the garden shop's profit (f(x)) increases, the construction material business's profit (g(x)) will decrease. This relationship holds true throughout the 15-year period.