Identify the end behaviour of of the following:

Question

Identify the end behaviour of

Note:

Please write neatly and clearly.

Grade 12 Advanced Function.

Answer 1

Hi,

when x approaches to the ±∞, in fact we are talking about end of behavior of function

1) factor of -3x⁴:

g(x)= -3x⁴( 1 - x³/-3x⁴ - 9x²/ -3x⁴ +2x/-3x⁴-3/-3x⁴)

g(x) = -3x⁴( 1 + 1/3x + 3/x² -2/3x^3 + 1/x^4)

when x approaches to the ±∞ we see g(x) = -3x⁴( 1 +0 +0 -0+0) = -3x⁴= -3(±∞)^4 = - ∞

so when x approaches to ±∞ function will be +∞ another meaning function goes to the

-∞ in 3th and 4th quadrant of coordinate plane.

I hope it is useful,

Minoo