Understanding Domain and Range in Linear Functions

When you're in Grade 9 Algebra I, it's super important to know about the domain and range of linear functions.

What is the Domain?

• The domain is basically the set of all possible inputs a function can take.
• For linear functions, the domain is usually all real numbers. This is written as: $$\text{Domain} = (-\infty, \infty)$$
• This means you can plug in any real number for $x$ in a linear equation, and you’ll get a straight line when you graph it.

What is the Range?

• The range is about the outputs of the function. These are the possible $y$ values that come from your function.
• For linear functions, the range is also: $$\text{Range} = (-\infty, \infty)$$
• This tells us that as $x$ changes to any real number, $y$ can also be any real number. This shows that linear equations go on forever in both directions.

Why Does This Matter for Graphing?

• Knowing the domain and range is really helpful when you’re drawing graphs.
• Take the linear function $y = 2x + 3$. When you graph it, you see a straight line that stretches infinitely in every direction.
• You'll also learn how changing the equation can affect its graph. This might include moving, stretching, or flipping the line, but it won’t change the domain or range.

In Conclusion:

• When you understand the domain and range, it helps you figure out how linear functions behave.
• This knowledge gives you a better grasp of how different parts of math connect with each other!