Question

How do you find the end behavior of `x^3-4x^2+7`?

Answer 1

End behavior : Down ( As `x -> -oo , y-> -oo` ),
Up ( As `x -> oo , y-> oo`),

Explanation:

`x^3-4 x^2+7`. The end behavior of a graph describes far left

and far right portions. Using degree of polynomial and leading

coefficient we can determine the end behaviors. Here degree of

polynomial is `3` (odd) and leading coefficient is `+`.

For odd degree and positive leading coefficient the graph goes

down as we go left in `3` rd quadrant and goes up as we go

right in `1` st quadrant.

End behavior : Down ( As `x -> -oo , y-> -oo`),

Up ( As `x -> oo , y-> oo`).

graph{x^3-4 x^2+7 [-20, 20, -10, 10]} [Ans]