Determine the end behavior of each rational function below. f(x) = 7x5 − 3x + 1 / 4x3 + 2
Accepted Solution
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Answer:When x ⇒ +∞ and x ⇒ -∞, f(x) ⇒ +∞Step-by-step explanation:Hi there!First, let´s write the function:f(x) = (7x⁵ - 3x +1) / (4x³ + 2) When x ⇒ +∞ f(x) ⇒ (7x⁵ - 3x) / 4x³ because (7x⁵ - 3x)>>>1 and 4x³>>>2 we can neglect those constants.f(x) ⇒7x⁵/4x³ - 3x/4x³ f(x) ⇒ 1.75x² - 0.75/x² (0.75/x² ⇒ 0 because a number divided by a very big number is approximately zero). Then:f(x) ⇒ 1.75x² ⇒ +∞When x ⇒ -∞f(x) ⇒ 1.75x² = +∞ (because x² is always positive)Then, when x ⇒ +∞ and x ⇒ -∞, f(x) ⇒ +∞