How do you find the end behavior and state the possible number of x intercepts and the value of the y intercept given #y=x^3-4x#?

1 Answer
Fleur
Jul 5, 2017

See the explanation below.

Explanation:

First, graph the function #f(x)=x^3-4x#.
graph{x^3-4x [-10, 10, -5, 5]}

From the graph, you can see as #x -> oo#, #f(x) -> oo#.
As #x->-oo#, #f(x) -> -oo#.

You can also write this using limits:

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

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

There are 3 #x#-intercepts here because there are 3 points where the graph intercepts the #x#-axis.

Similarly, you can find the #y#-intercept graphically if you find the point where the graph intercepts the #y#-axis. In this case, the #y#-intercept is 0.

If you want to find the #y#-intercept algebraically, substitute 0 in for x.

#y=x^3-4x#
#y=0^3-4(0)#
#y=0#

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