Plotting Functions on a Graph

Graphs are powerful tools for visualizing how functions behave. The graph of a function is a picture of all the points \((x, y)\) where \( y = f(x) \).

Steps to Graph a Function

1. Make a table of \( x \) values and their corresponding \( y \) values.
2. Plot each point \((x, y)\) on the coordinate plane.
3. Connect the dots in a smooth curve or straight line, depending on the function.

The Vertical Line Test

If any vertical line crosses the graph more than once, it's not a function!

Why Graphs Matter

Graphs show trends, patterns, and help us predict values. You can see where a function increases, decreases, or stays the same.

Fun Fact

Graphs are everywhere, from weather charts to video game scoring!