Question

What is the end behavior of the function f(x)=54x3? As x→∞, f(x)→−∞ As x→−∞, f(x)→−∞ As x→∞, f(x)→∞ As x→−∞, f(x)→−∞ As x→∞, f(x)→−∞ As x→−∞, f(x)→∞ As x→∞, f(x)→∞ As x→−∞, f(x)→∞

Answer 1

As x→∞, f(x)→∞ is correct, also As x→−∞, f(x)→−∞.

Explanation:

This function is a simple modification of the basic function y = x^3, which goes to infinity in Quadrant I as x increases, and to negative infinity in Quadrant II as x decreases. As x→∞, f(x)→∞ is correct, also As x→−∞, f(x)→−∞.

The same end behavior applies to f(x) = 54x^3.