Find the power function that the graph of f resembles for large values of |x|.
-$$f ( x ) = - x ^ { 2 } ( x + 4 ) ^ { 3 } \left( x ^ { 2 } - 1 \right)$$
A) $y = x ^ { 3 }$
B) $y = x ^ { 2 }$
C) $y = - x ^ { 7 }$
D) $y = x ^ { 7 }$

Question

Quizplus · Accepted Answer

The power function that the graph of $f$ resembles for large values of $|x|$ is determined by the highest power of $x$ in the expanded form of the function. For $f(x) = -x^2(x + 4)^3(x^2 - 1)$, the highest power of $x$ comes from multiplying the powers of $x$ in each factor: $2 + 3 + 2 = 7$. The leading coefficient is negative, so the correct power function is $y = -x^7$.

Find the Power Function That the Graph of F Resembles f(x)=−x2(x+4)3(x2−1)f ( x ) = - x ^ { 2 } ( x + 4 ) ^ { 3 } \left( x ^ { 2 } - 1 \right)f(x)=−x2(x+4)3(x2−1)

Find the Power Function That the Graph of F Resembles $f ( x ) = - x ^ { 2 } ( x + 4 ) ^ { 3 } \left( x ^ { 2 } - 1 \right)$