Question

Is a linear function subtracted from a cubic function is a cubic function?

Answer 1

Subtracting a linear function from a cubic function results in a cubic function because the cubic term remains unchanged, as the linear function does not contain any cubic terms to cancel it out.

Step-by-step explanation:

When a linear function is subtracted from a cubic function, the result is still a cubic function. This is because the highest degree term (the cubic term) remains unaltered. In a cubic function, the leading term is of the form ax3, where a is a non-zero constant, which defines the cubic nature of the function. A linear function, on the other hand, has a leading term of the form bx, where b is a constant. When we subtract the linear function from the cubic, the cubic term is unaffected because there are no cubic terms in a linear function to cancel it out.

For example, consider the cubic function f(x) = 2x3 + 3x2 - x + 5 and the linear function g(x) = 4x + 1. Subtracting g(x) from f(x) gives us f(x) - g(x) = (2x3 + 3x2 - x + 5) - (4x + 1) = 2x3 + 3x2 - 5x + 4, which is still a cubic equation due to the presence of the 2x3 term.

Answer 2

yes

Step-by-step explanation:

You subract like terms. A cubic function has x^3 while the highest power of x in a linear function is only 1. You cannot subtract x from x^3 so a linear function subtracted from a cubic function remains a cubic function.