Final answer:
The student's question revolves around a function f(x) with factors x, x-5, and x+2, and the properties and solutions of equations involving constants and variables. The value and slope of f(x) at a specific point (x = 3) were also discussed.
Step-by-step explanation:
Considering the provided factors of a function f(x), it can be determined that the function has x, x-5, and x+2 as its factors. To understand this better, each factor should be looked at separately while keeping the other factors constant. This implies that the function f(x) can be expressed as f(x) = x * (x - 5) * (x + 2). Multiplying these factors yields a polynomial.
Discussing the relation between variables and constants, we touched upon the notion that the product of a function f multiplied by another value results in a constant. This means if the value of f is smaller, the other value must be larger to maintain the constant product, and vice versa. Additionally, the concept of raising numbers to a power was mentioned, highlighting a strategy to simplify expressions and solve equations.
Moreover, the function f(x) was analyzed at x = 3, where it has a positive value and a positive, decreasing slope. From the options provided, y = x² could likely correspond to f(x) since a quadratic function has a positive slope that decreases as x increases.