Lesson Notes By Weeks and Term v4 - SHS 1
APPLICATIONS OF ALGEBRA
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APPLICATIONS OF ALGEBRA
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Subject: Additional Mathematics
Class: SHS 1
Term: 1st Term
Week: 17
Grade code: 1.1.2.LI.1
Strand code: 1
Sub-strand code: 2
Content standard code: 1.1.2.CS.1
Indicator code: 1.1.2.LI.1
Theme: MODELLING WITH ALGEBRA
Subtheme: APPLICATIONS OF ALGEBRA
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This lesson introduces rational functions, which are a fundamental concept in algebra. Just as a rational number is a ratio of two integers (like 3/4), a rational function is a ratio of two polynomials. Understanding rational functions is crucial because they model many real-world situations, from calculating the average cost of producing goods at a small business in Kaneshie Market to determining the concentration of medicine in a patient's bloodstream over time. By learning to identify the "rules" of these functions—their domain (what inputs are allowed) and their zeros (where they equal zero)—we gain the power to analyse and solve complex real-life problems.
Part 1: Revisiting Polynomials
Before we can understand rational functions, we must remember what a polynomial is.
A polynomial is an algebraic expression made up of variables and coefficients, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents. Examples of Polynomials: `P(x) = 5` (a constant polynomial) `P(x) = 2x + 3` (a linear polynomial) `P(x) = x² - 4x + 7` (a quadratic polynomial) `P(x) = 4x³ - 9` (a cubic polynomial) Examples of expressions that are NOT Polynomials: `f(x) = √x` (because the exponent is 1/2, which is not an integer) `g(x) = 3/x` (because this is `3x⁻¹`, which has a negative exponent) Part 2: What is a Rational Function?
The word "rational" comes from "ratio". A rational function is simply a function that is a ratio of two polynomials.