What is the end behavior of #f(x) = x^3 + 4x#?

2 Answers
Jul 15, 2018

Answer:

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

Up ( As #x -> oo , y-> oo# )

Explanation:

#f(x)= x^3 + 4 x# 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 [-20, 20, -10, 10]} [Ans]

Jul 15, 2018

Answer:

#lim_(xtooo) f(x)=oo#

#lim_(xto-oo)f(x)=-oo#

Explanation:

To think about end behavior, let's think about what our function approaches as #x# goes to #+-oo#.

To do this, let's take some limits:

#lim_(xtooo) x^3+4x=oo#

To think about why this makes sense, as #x# balloons up, the only term that will matter is #x^3#. Since we have a positive exponent, this function will get very large quickly.

What does our function approach as #x# approaches #-oo#?

#lim_(xto-oo) x^3+4x=-oo#

Once again, as #x# gets very negative, #x^3# will dominate the end behavior. Since we have an odd exponent, our function will approach #-oo#.

Hope this helps!