Question

What is the end behavior of the graph of the polynomial function y = 7x12 – 3x8 – 9x4?. . x -> ___ y->__ and as x-> ___ y->___

Answer 1

We are given with the polynomial above and is asked to evaluate the end behavior of the function.  The end behavior of a polynomial function is the behavior of the graph of f ( x ) as x approaches positive infinity or negative infinity. As x approaches negative infinity, the function goes to negative infinity while when x approaches positive infinity, the function goes to positive infinity 

Answer 2

Answer:

As x ----> ∞, y----> ∞

As x ----> -∞, y----> ∞

Step-by-step explanation:

y = 7x^12 – 3x^8 – 9x^4

To find the end behaviour, we look at the leading coefficient and the largest exponent

In the given equation, the largest exponent is 12 that is an even number

the leading term is 7x^12, so leading coefficient is +7

When the largest exponent is even and leading coefficient is positive then the graph of y goes up(to infinity) on the left as well as on the right side of x

As x ----> ∞, y----> ∞

As x ----> -∞, y----> ∞