Graphing is a great way to see the domain and range of a function.

Understanding Domain and Range

• Domain: This is all the possible input values (x-values) for a function.

  For example, in the function ( f(x) = \sqrt{x} ), the domain is ( x \geq 0 ).

  That means you can only use zero and positive numbers because you can’t take the square root of a negative number.

• Range: This is all the possible output values (y-values).

  In the same function ( f(x) = \sqrt{x} ), the range is also ( y \geq 0 ).

How Graphing Helps

1. Visual Representation: When you draw the graph of a function, you can easily see where the graph starts and where it ends on both the x-axis (horizontal) and y-axis (vertical).

   This gives you a clear view of the domain and range.

2. Identifying Restrictions: For functions like ( f(x) = \frac{1}{x} ), the graph shows that the function doesn’t work at ( x=0 ).

   So, the domain is written as ( (-\infty, 0) \cup (0, \infty) ). This means you can use all numbers except zero.

Conclusion

Using graphs helps us understand how functions behave.

It makes it easier to learn about domain and range!