State the end behaviours of the polynomial function of the following:

Question

State the end behaviours of the polynomial function 

Note:

Please write neatly and clearly.

Grade 12 Advanced Function.

Answer 1

Hi,

 

1) factor:

  = x [ 3x(1-4/3x )][-2x(1-1/2x)] [ x(1 -5/x)]= -6x⁴(1-4/3x )(1-1/2x)(1 -5/x)

when x approaches to the ±∞ you see:

g(x) = -6x⁴( 1-0)(1-0)(1-0) = -6x⁴= -6(±∞)4 = - ∞

I hope it is useful,

Minoo