Find the power function that the graph of f(x) resembles for larger values of |x|.

Question

f(x)=1/2(x+3)(x+1)^2(x-2)

Answer 1

Dear Jillian,

in such a function, for larger values of |x|, we can omit the constants in each factor.

Meaning, for larger values of |x|,

(x + 3) can be approximated with x

(x + 1)² with x²

(x - 2) with x

Therefore,

f(x) ≈ (1/2) (x) (x)²(x) = (1/2) x⁴