Question

Determine the end behavior, number of zeros, and maximum number of turns for the given function.

h(x)=3x^3-2x^2-12x+8

Answer 1

the end behavior of h(x) matches the end behavior of x

3 zeros, 2 turns

Explanation:

The polynomial is of degree 3, so will have a maximum of ...

• 3 zeros
• 3-1 = 2 turns

Because the degree is odd the signs of the end values of h(x) will be different. Because the leading coefficient is positive, the signs of the end values of h(x) will match the sign of x:

• as x → -∞, h(x) → -∞
• as x → ∞, h(x) → ∞