Find the power function that the graph of f resembles for large values of |x|.
-$$f ( x ) = ( x + 12 ) ^ { 6 } ( x - 3 ) ^ { 3 }$$
A) $y = x ^ { 6 }$
B) $y = x ^ { 3 }$
C) $y = x ^ { 18 }$
D) $y = x ^ { 9 }$

Question

Quizplus · Accepted Answer

For large values of |x|, the dominant term in the polynomial is determined by the highest degree term. The function $f(x) = (x + 12)^6 (x - 3)^3$ expands to a polynomial where the highest degree term is $x^9$. Thus, the graph of $f$ resembles $y = x^9$ for large values of |x|.

Find the Power Function That the Graph of F Resembles f(x)=(x+12)6(x−3)3f ( x ) = ( x + 12 ) ^ { 6 } ( x - 3 ) ^ { 3 }f(x)=(x+12)6(x−3)3

Find the Power Function That the Graph of F Resembles $f ( x ) = ( x + 12 ) ^ { 6 } ( x - 3 ) ^ { 3 }$