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

Question

Sadie Alexander · Accepted Answer

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

#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]

Chloe Alexander · Answer

undefined To find the end behavior of the function $ f(x) = x^3 - 4x^2 + 7 $, observe the leading term $ x^3 $. As $ x $ approaches positive or negative infinity, the dominant term $ x^3 $ determines the behavior of the function. Since the coefficient of $ x^3 $ is positive, the end behavior is as follows:

- As $ x $ approaches positive infinity, $ f(x) $ increases without bound.
- As $ x $ approaches negative infinity, $ f(x) $ decreases without bound.