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: 12
Grade code: 1.1.2.LI.7
Strand code: 1
Sub-strand code: 2
Content standard code: 1.1.2.CS.1
Indicator code: 1.1.2.LI.7
Theme: MODELLING WITH ALGEBRA
Subtheme: APPLICATIONS OF ALGEBRA
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This lesson introduces the concept of composite functions. We will explore how functions can be combined, not by adding or multiplying them, but by applying one function to the result of another. Think of it like a production line: cocoa beans are harvested (first function), and then the harvested beans are fermented (second function). The final product depends on both processes happening in sequence. This concept of "function of a function" is a powerful tool in mathematics and has many real-world applications, from calculating currency exchange rates to understanding multi-step processes in science and economics.
A. Refresher: What is a Function? A function is like a machine or a rule. It takes an input (usually `x`), performs an operation on it, and produces a single output (usually `f(x)` or `y`). Example: If `f(x) = 2x + 5`: If the input is `x = 3`, the output is `f(3) = 2(3) + 5 = 6 + 5 = 11`. If the input is `x = a`, the output is `f(a) = 2a + 5`.
B. Defining Composite Functions A composite function is created when you link two or more functions together in a sequence. The output of the first function becomes the input for the second function.
Imagine two machines: Machine `g`: Takes an input `x` and produces an output `g(x)`. Machine `f`: Takes the output from Machine `g`, which is `g(x)`, and uses it as its input to produce a final output `f(g(x))`.
This entire two-step process is a single composite function.