(a) Describe the end behavior of the polynomial function. End behavior: y → as x → ∞ y → as x → −∞

Question

P(x) = x(x² − 4)

Answer 1

P(x) = y = x(x^2-4) = x^3 -4x

as x approaches infinity, y approaches infinity

as x approaches negative infinity, y approaches negative infinity

the highest powered term dominates, x^3. (infinity)^3 = infinity, (-infinity)^3 = -infinity

Answer 2

f(x) = x³ - 4x

Odd degree polynomials with a positive leading coefficient go to - infinity as x approaches - infinity. They go to + infinity as x approaches + infinity.

y → ∞ as x → ∞

y → - ∞ as x → - ∞

You can also graph it to see the end behavior.

https://www.purplemath.com/modules/polyends.htm