Key Differences Between Domain and Range in Functions

1. What They Mean:

   • Domain: This is all the possible input values you can use in a function. Think of input as what you put into a machine. For example, in the function ( f(x) = \sqrt{x} ), the domain is all numbers ( x ) that are 0 or greater.
   • Range: This is all the possible output values you get from the function. It’s like what comes out of the machine after you put something in. For the same function, the range is also all numbers ( f(x) ) that are 0 or greater.

2. How They Are Notated:

   • Domain: It’s often shown as ( D(f) ). For example, you may see ( D(f) = [0, \infty) ), which means all numbers from 0 to infinity.
   • Range: It’s often shown as ( R(f) ). Similarly, you might see ( R(f) = [0, \infty) ), meaning all numbers from 0 to infinity.

3. How to Visualize Them:

   • The domain is the width of a graph, which is how far it goes from side to side.
   • The range is the height of a graph, showing how far it goes up and down.

Knowing these ideas is important for understanding functions in Year 11 Math.