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Introduction to Polynomial and Rational Functions

Introduction to Polynomial and Rational Functions — from OpenStax Precalculus 2e.

Introduction to Polynomial and Rational Functions

You don't need to dive very deep to feel the effects of pressure. As a person in their neighborhood pool moves eight, ten, twelve feet down, they often feel pain in their ears as a result of water and air pressure differentials. Pressure plays a much greater role at ocean diving depths.

Scuba and free divers are constantly negotiating the effects of pressure in order to experience enjoyable, safe, and productive dives. Gases in a person's respiratory system and diving apparatus interact according to certain physical properties, which upon discovery and evaluation are collectively known as the gas laws. Some are conceptually simple, such as the inverse relationship regarding pressure and volume, and others are more complex. While their formulas seem more straightforward than many you will encounter in this chapter, the gas laws are generally polynomial expressions.

Introduction to Polynomial and Rational Functions

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What is a function, really?

A rule that assigns exactly one output to each input. The vertical-line test on a graph is the same idea: no input may have two outputs.

Why do we need complex numbers?

Because x² + 1 = 0 has no real solution, and allowing one new number i with i² = −1 makes every polynomial equation solvable. They then turn out to describe rotation, waves and alternating current more naturally than real numbers do.

Àwọn ààyè ojú-ìwé yìí tí a fi pamọ́ láti OpenStax College Algebra 2e (CC BY-NC-SA 4.0), OpenStax Precalculus 2e (CC BY-NC-SA 4.0). Tí a fi pamọ́ síì níbẹ̀; àwọn àwọn àṣiṣe ní wa. Nítorí pé a tí fi àkóónú rẹ̀ pamọ́ fún ìlòjónú tí kò jẹ́ iṣẹ́ ọ̀fẹ́, ìwé-ìwé yìí jẹ́ ọ̀fẹ̀, kò ní ìfilọ́wọ́, àti àwọn tí a ti pamọ́ fún ìlòjónú kan.

Diẹ̀ nínú Precalculus

Complex numbers Polynomial functions Rational functions Sequences and series The binomial theorem Conic sections Vectors Exponential and logarithmic functions Polynomial division and the remainder theorem Parametric equations and polar coordinates