Question

How do you find the end behavior of `y=5-x^4`?

Answer 1

The graph is down on both ends.

Explanation:

The end behavior of the graph of a function is determined by its degree and the sign of its leading coefficient, there are 4 possible scenarios as follow:

1) Even power with positive leading coefficient: up on both ends.

2) Even power with negative leading coefficient: down on both ends.

3) Odd power with positive leading coefficient: down on left side, up on right side.

4) Odd power with negative leading coefficient: up on left side, down on right side.

So in this case we rewrite the function in standard form as follow :

`y= -x^4 +5`

2nd scenario from the above table applies here therefore the graph is down on both ends.