Final answer:
The equation 7 = 3x² - 9x + 20 represents both a relation and a function, as it satisfies the definitions of each concept by having each x-value correspond to exactly one y-value.
Step-by-step explanation:
The equation in question is 7 = 3x² - 9x + 20. To determine whether this is a relation, a function, or neither, we must understand these concepts. A relation is any set of ordered pairs, while a function is a special type of relation where each input (x-value) corresponds to exactly one output (y-value).
In this case, the equation can be rewritten in the form of y = 3x² - 9x + 13, where 7 has been subtracted from both sides. This represents a quadratic equation, and for each x-value, we can solve to find exactly one corresponding y-value. Therefore, this equation does represent both a relation and a function because it satisfies both definitions.
The correct answer to the question is (b) both a relation and a function.