What is the end behavior of the graph of the polynomial function y = 7x¹² - 3x⁸ - 9x⁴?

Solution:

To find the end behaviour of a function, we must only consider the highest degree term

Given:

Polynomial y = 7x¹² - 3x⁸ - 9x⁴

Here we have to consider 7x¹²

7 is a positive coefficient of x¹²

So if x goes to positive high numbers the answer will be positive high numbers

x → ∞, y → ∞

So if x goes to negative high numbers the answer will be positive high numbers due to the even powers which act on x

x → -∞, y → ∞

Therefore, the end behaviour of the graph is x → ∞, y → ∞ and x → -∞, y → ∞.

What is the end behavior of the graph of the polynomial function y = 7x¹² - 3x⁸ - 9x⁴?

Summary:

The end behavior of the graph of the polynomial function y = 7x¹² - 3x⁸ - 9x⁴ is x → ∞, y → ∞ and x → -∞, y → ∞.