Question

Determine the end behavior of each rational function below. Graph each function on the graphing calculator, and

explain how the graph supports your analysis of the end behavior.
a. f(x) = x2 − 3 / x3
b. f(x) = x2 − 3 / x2 + 1
c. f(x) = x3 / x2 − 3

Answer 1

a) End behavior: As → ∞, () → . As → −∞, () → .

Looking at the ends of the graph, as goes to ∞ or −∞, gets

closer to .

b) End behavior: As → ∞, () → . As → −∞, () → .

Looking at the ends of the graph, as x goes to ∞ or −∞, gets

closer to .

c) End behavior: As → ∞, () → ∞, and as → −∞, () → −∞.

Looking at the ends of the graph, as goes to ∞, continues to increase

toward ∞, and as x goes to −∞, continues to decrease toward −∞.

Obs:. Graphics are attached