Short Answer 
The domain of a function encompasses all possible values for its independent variable, such as lists, numerical sets, or continuous ranges. The range represents the potential output values, while it’s crucial to recognize that predictions can only be made accurately within the established domain, as values outside this range may lead to unreliable outcomes.
Step 1: Understand Domain
The term domain in mathematics is the complete set of possible values for the independent variable of a function. This can be a variety of forms, such as:
- List of majors at a university, e.g., X = {English, Mathematics, Science}
- Numerical sets, e.g., Y = {0, 1, 2, …}
- Continuous ranges like Z, which could include any amount of money starting from zero
Step 2: Comprehend Range
The range of a function defines all possible output values after conducting an experiment or survey. It provides insight into the results that can be achieved, such as:
- Hair colors as outputs, e.g., black, blond, gray, green, orange
- Possible results of a study conducted on survey responses
- Set of potential grades based on a scoring system
Step 3: Recognize Predictions Outside the Domain
When considering specific values that a function can take, it’s important to note that only values within the domain yield reliable predictions. For example, if the domain is limited to a certain range, any outlier, such as 90 in a range of 65 to 75, falls outside that domain and cannot be accurately predicted. Always ensure to check reliability based on domain constraints.