Question

What is the "rate of change" of a function?

Answer 1

Rate of change is a number that tells you how a quantity changes in relation to another.
Velocity is one of such things. It tells you how distance changes with time.
For example: 23 km/h tells you that you move of 23 km each hour.

Another example is the rate of change in a linear function.

Consider the linear function: `y=4x+7`
the number 4 in front of `x` is the number that represent the rate of change. It tells you that every time `x` increases of 1, the corresponding value of `y` increases of 4.
If you get a negative number it means that the `y` value is decreasing.
If the number is zero it means that you do not have change, i.e you have a constant!

Examples: