Welcome to learning functions! A function is like a special machine. You put an input in, the machine follows a rule, and gives you exactly one output. The most important rule is: one input always gives one unique output. Let's see how this works with an example.
Now let's learn how to write functions. There are two common ways: y equals 2x plus 1, or f of x equals 2x plus 1. The notation f of x means 'the output when the input is x'. Let's practice calculating some values.
The simplest functions are linear functions. They have the form f of x equals a x plus b. Here, a is the slope which controls how steep the line is, and b is the y-intercept where the line crosses the y-axis. Let's see how the point moves along our example function f of x equals 2x plus 1.
To check if a graph represents a function, we use the vertical line test. Draw vertical lines through the graph. If any vertical line touches the graph at more than one point, then it's not a function. Let's test this with two examples.