Functions: Domain and Range Basics

Domain and Range of a Function

• The domain of a function is the set of all possible input values (x-values) that will produce a real output (y-value).
• The range of a function is the set of all possible output values (y-values) that result from the input values (x-values).

Function Definition

• A function is a relationship between an input (x-value) and an output (y-value). A function assigns exactly one output value to each input value.
• Sets of inputs (x-values) and outputs (y-values) are often written as ordered pairs or can be illustrated by a mapping diagram.

Cartesian Coordinate Plane

• Rene Descartes developed the Cartesian coordinate system.
• The coordinate system is a two-dimensional plane formed by two perpendicular number lines, the x-axis and the y-axis.
• The point of intersection between the two axes is called the origin.

Linear Equations vs. Linear Inequalities

• The symbol = is used for linear equations.
• The symbols >, <, ≥, and ≤ are used for linear inequalities.
• A linear equation represents a straight line on a graph.
• A linear inequality represents a region on a graph, often with a boundary line.

Solving Linear Inequalities

• The key to solving inequality equations rests on the fact that inequalities follow similar rules as equations, with one exception: when an inequality is multiplied or divided by a negative number, the inequality sign must be reversed.

Linear Function vs. Non-linear Function

• Linear functions are represented as y = mx + b, where m is the slope and b is the y-intercept.
• Non-linear functions have a relationship that isn't a straight line and don't follow the form of ax + b.

Problem-Specific Information

• A dozen short pants (s) added to half a dozen of pajamas (p) has a total cost greater than or equal to Php 960 can be expressed as 12p + 6s ≥ 960.
• The square of 49 is 2,401.
• The square of 16 is 256.
• One of the symbols that is not used in linear inequalities is the equal symbol.