Final answer:
To find the domain of a function, consider all x-values that do not result in undefined operations. To determine the range, analyze the possible y-values from the function. An example would be f(x) = x^2 with a domain of all real numbers and a range of non-negative real numbers.
Step-by-step explanation:
The domain and range of a function are critical concepts in mathematics that speak to the set of all possible input values (domain) and the set of all possible output values (range) that the function can take on.
To determine the domain of a function, we consider all possible x-values that we can plug into the function without causing any undefined operations, such as division by zero or taking the square root of a negative number in the real number system.
To find the range of a function, we need to look at the possible y-values that can result from substituting valid x-values into the function. This often involves analyzing the behavior of the function and the y-values it can take on.
For example, consider the function f(x) = x2. The domain is all real numbers because you can square any real number. However, the range is only the set of non-negative real numbers because squaring any real number cannot yield a negative result.