Question

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)`

Answer 1

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!