Question

Complete the end behavior statement for the function shown above. As x→−∞, f(x)→

Answer 1

Given:

$f(x)=\frac{-9x^7}{3x^7}$

Required:

$We\text{ need to find the end behavior of f\lparen x\rparen as x}\rightarrow-\infty.$

Explanation:

We know that the end behavior of a function is the behavior of the graph of f(x) as x approaches negative infinity.

Consider the given function.

$f(x)=\frac{-9x^7}{3x^7}$

Take limit on both sides.

$\lim_{x\to-\infty}f(x)=\lim_{x\to-\infty}(\frac{-9x^7}{3x^7})$

Cancel out the common multiple.

$\lim_{x\to-\infty}f(x)=\lim_{x\to-\infty}(\frac{-9}{3})$

$\lim_{x\to-\infty}f(x)=\frac{-9}{3}$

$\lim_{x\to-\infty}f(x)=-3$

The end behavior of f(x) is -3as x approaches negative infinity

Final answer:

$As\text{ x}\rightarrow-\infty,f(x)=-3$