Finding the domain of a function from its graph involves identifying all the possible input values (usually x-values) that the function can accept. Here are the key steps to determine the domain:
- Examine the x-axis: Look closely at the x-axis of the graph. The domain consists of all the x-values where the graph exists.
- Identify endpoints: If the graph starts or ends at specific points, include those x-values as part of the domain. If the graph has open circles (indicating not included), those points should be excluded from the domain.
- Check for gaps or discontinuities: Look for any breaks or jumps in the graph. If there are sections where the graph does not exist, such as asymptotes or undefined points, those x-values should be excluded from the domain.
- Consider continuous intervals: If the graph is continuous between two points, all x-values between those points are included. Write the domain in interval notation accordingly.
For instance, if a graph shows a curve that goes from x = -3 to x = 2, with a hole at x = 0, you would express the domain as: (-3, 0) ∪ (0, 2]. This indicates that the domain includes all x-values from -3 to 2, except for 0, which is not included.