Sketch, find the end behavior(EB), y- int, zeros, and multiplicities?

#y=1/36(x^2 -6)^2(x+1)^2(x^2-3x-4)(3-2x)^3(x^2+1)(x^2-4x-1)#

1 Answer
Dec 17, 2017

The highest degree is #14#, and the leading coefficient is positive, therefore, the #lim_(x-> -oo) = lim_(x->+ oo) = +oo#.

The y-intercept can be found by plugging in #x = 0#, getting #y = 108#.

The zeroes can be found by setting the function equal to #0# and solving for #x#. I won't do all of them but for instance if

#0 = 1/36(x^2 - 6)^2(x - 2)#

Then #x^2 - 6 = 0 -> x = +- sqrt(6)# and #x = 2#.

Multiplicities are the degree of each #0#. For instance, in #y =1/36(x^2 - 6)^2(x -2)# , then #(x^2 - 6)^2# has degree #2# and #x - 2# has degree #1#, because of the exponents.

Hopefully this helps!