Lesson Notes By Weeks and Term v5 - Grade 9

Lesson Video

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Performance objectives

• Define a function and identify input/output variables.
• Represent linear functions using equations, tables, and graphs.
• Sketch graphs of linear functions (y = mx + c).
• Recognize simple non-linear functions (parabolas and hyperbolas).
• Interpret graphs to solve problems.

Lesson summary

This week, we'll be diving into the fascinating world of functions and graphs. Functions are like mathematical machines – you put something in (an input), and you get something else out (an output), following a specific rule. Representing these relationships visually using graphs helps us understand and predict patterns in various situations. Understanding functions and graphs is crucial for many real-world applications, from calculating cellphone data usage to predicting population growth or understanding the trajectory of a cricket ball.

Lesson notes

What is a Function? A function is a relationship between two sets of values, where each input value (often represented by 'x') corresponds to exactly one output value (often represented by 'y'). We write this relationship as y = f(x), where 'f' is the name of the function. 'x' is called the independent variable, and 'y' is called the dependent variable because its value depends on the value of 'x'.

Example: Imagine buying airtime. The amount of airtime you get (y) is a function of the amount of money you spend (x). For every amount you spend, you get a specific amount of airtime.

Linear Functions: Straight Lines A linear function is a function whose graph is a straight line.

The general form of a linear function is: y = mx + c Where: m is the gradient (or slope) of the line. It tells us how steep the line is and whether it's increasing or decreasing. A positive 'm' means the line goes upwards as you move from left to right. A negative 'm' means the line goes downwards.

The gradient is calculated as: m = (change in y) / (change in x) = (y₂ - y₁) / (x₂ - x₁) c is the y-intercept. It is the point where the line crosses the y-axis (where x = 0). The coordinates of the y-intercept are (0, c).