Question

Determine which of the following statements is true for the function g(x) = 4x^5 - 3x^6 + 2x^3 - 1.

A. As x increases, y increases. As x decreases, y decreases.

B. As x increases, y increases. As x decreases, y increases.

C. As x increases, y decreases. As x decreases, y increases

D. As x increases, y decreases. As x decreases, y decreases

Answer 1

Option D. As x increases, y decreases. As x decreases, y decreases

Explanation:

we have the function

`g(x)=4x^(5)-3x^(6)+2x^(3)-1`

we know that

g(x) is a polynomial of sixth degree

The value of the function will approach the same negative infinity for large positive or negative x. That infinity is determined by the sign of the coefficient of the 6th-degree term, which is negative.

therefore

As x increases -----> The value of y decreases

As x decreases ----> The value of y decreases