Question

If the cubic function P(x) includes the points (−4, 0), (0, 0), and (2, 0), which of the following represents this function?

Answer 1

The function cannot be determined with the given information.

Step-by-step explanation:

The given points (-4, 0), (0, 0), and (2, 0) indicate that the function is a cubic function with three real roots. A cubic function is of the form P(x) = ax^3 + bx^2 + cx + d. Since the function passes through the x-axis at (-4, 0), (0, 0), and (2, 0), the roots of the cubic function are -4, 0, and 2. Therefore, the function can be written as P(x) = a(x + 4)(x - 0)(x - 2). However, since a cubic function with three real roots has an odd degree, the coefficient 'a' must be negative or positive. This means that the function can also be written as P(x) = -a(x + 4)(x - 0)(x - 2) or P(x) = a(x + 4)(x - 0)(x - 2). So, the correct representation of the function cannot be determined with the given information.

Answer 2

We observe that the function has the following behavior:
x y
-4 0
0 0
2 0
Therefore, the function that best suits this behavior is:
P (x) = 0
This function is the same as a horizontal line along the entire x axis.
Answer:
P (x) = 0
Horizontal line along the x axis.