Question

Question 12 (5 points)SavedDescribe the end behavior of the graph of f(x)= x^3(x+ 3)(-5x + 1) using limits.

Answer 1

`\begin{gathered} \lim_(x\to-\infty)x^3(x+3)(-5x+1)=\lim_(x\to-\infty)x^3\lim_(x\to-\infty)(x+3)\lim_(x\to-\infty)(-5x+1) \\ \lim_(x\to-\infty)x^3=-\infty \\ \lim_(x\to-\infty)(x+3)=-\infty \\ \lim_(x\to-\infty)(-5x+1)=\infty \\ \therefore\lim_(x\to-\infty)f(x)=\infty \\ \lim_(x\to\infty)x^3(x+3)(-5x+1)=\lim_(x\to\infty)x^3\lim_(x\to\infty)(x+3)\lim_(x\to\infty)(-5x+1) \\ \lim_(x\to\infty)x^3=\infty \\ \lim_(x\to\infty)(x+3)=\infty \\ \lim_(x\to\infty)(-5x+1)=-\infty \\ \therefore\lim_(x\to\infty)f(x)=-\infty \end{gathered}`

Answer: Third option