๐ Graph of a Function
7th Grade Algebra
A graph of a function is a visual picture that shows how two quantities are related. It turns a formula into a drawing you can see and analyze!
๐ 1. Coordinate Plane Review
The coordinate plane is formed by two perpendicular number lines:
- Horizontal line โ x-axis
- Vertical line โ y-axis
- Intersection point โ Origin O(0, 0)
Key idea: Every point on the plane has coordinates (x, y) โ an ordered pair. The x-coordinate shows the horizontal position, and the y-coordinate shows the vertical position.
Example: If x = 2 and y = 5, the point is written as (2, 5). Move 2 units right, then 5 units up.
Interactive Coordinate Plane
Interactive visualization โ available in the full lesson
Interactive visualization โ available in the full lesson
๐ 2. Definition: What is a Graph of a Function?
Definition: The graph of a function is the set of all points on the coordinate plane whose x-coordinates equal the values of the argument, and whose y-coordinates equal the corresponding values of the function.
In other words: The graph of a function y = f(x) is the set of all points (x, y) on the coordinate plane where x is a value of the argument (from the domain) and y is the corresponding function value f(x).
In simpler words: for every allowed x, we compute y = f(x), and the point (x, y) is on the graph. The collection of all such points forms the graph.