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
Apr 10, 2018

Answer:

See below.

Explanation:

To find the end behaviour of a polynomial, we only need to look at the degree and leading coefficient of the polynomial. The degree is the highest power of #x# in this case.

#-x^3#

We now see what happens as #x->+-oo#

as #x->oo# , # \ \ \ \ \ \ \ \ \ \ \ -x^3->-oo#

as #x->-oo# , # \ \ \ \ \ \ -x^3->oo#

#y# axis intercepts occur where #x=0#:

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

Coordinates:

#color(blue)( (0 ,0)#

#x# axis intercepts occur where #y=0#

#-x^3-4x=0#

#x^3+4x=0#

Factor:

#x(x^2+4)=0#

#x=0#

#x^2+4=0# ( this has no real solutions ).

coordinates:

#color(blue)(( 0 , 0 )#

The graph confirms these findings:

graph{y=-x^3-4x [-16.01, 16.02, -20,20]}