How do you find the end behavior of #y=5-x^4#?
The graph is down on both ends.
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 :
2nd scenario from the above table applies here therefore the graph is down on both ends.