In Grade 12 Algebra I, it's really important to understand the domain and range of functions. These concepts help us define functions correctly.

What are Domain and Range?

• Domain: This is all the possible input values (usually $x$ values) that you can use for a function. For example, in the function ( f(x) = \sqrt{x} ), the domain is $x \geq 0$. This means you can use any number from $0$ to infinity.

• Range: This is all the possible output values (usually $y$ values) that a function can produce. In the same function ( f(x) = \sqrt{x} ), the range is also $y \geq 0$. So, the output will also be any number from $0$ to infinity.

Why Do Domain and Range Matter?

1. Uniqueness: For something to be called a function, each input from the domain must lead to only one output in the range. We can check this with a test called the “vertical line test.” If a vertical line hits the curve more than once, then it’s not a function.

2. Real-World Situations: Knowing the domain and range helps you model real-life scenarios better. For example, it can help you figure out the right prices in economics or understand limits in geometry.

Understanding these ideas is key. It helps you with function notation, graphing, and solving equations, making advanced math easier to handle.