Answer:
B) The sum is linear and the product is quadratic.
D) The sum has one y-intercept and the product has two x-intercepts.
Explanation:
The sum of two linear functions products another linear function. Therefore, s(x) is a linear function.
The product of two linear functions produces a quadratic function. Therefore, p(x) is a quadratic function.
The rate of change of a quadratic function is not constant because its graph is a curve, so both functions do not have a constant rate of change.
From the given table, we can see that the values of s(x) are the same for all values of x. This indicates that the sum of the two linear functions produces a horizontal line (parallel to the x-axis), at y = -1. Therefore, s(x) does not intercept the x-axis at all.
As s(x) is a horizontal line at y = -1, it has one y-intercept at y = -1.
The x-intercepts are the values of x when y = 0. From the given table, we can see that there are two points when p(x) = 0. Therefore, p(x) has two x-intercepts.
As s(x) is a horizontal line, it is constant for all values of x. Therefore, it does not decrease for x ≥ 2.
Therefore, the statements that correctly compare the sum and product are:
- B) The sum is linear and the product is quadratic.
- D) The sum has one y-intercept and the product has two x-intercepts.