The domain of a function is the set of all possible input values for which the function is defined. In other words, it is the set of all x-values that can be plugged into the function to produce a valid output.
To find the domain of a function, you must first identify any restrictions on the input values. This can include restrictions such as division by zero or taking the square root of a negative number. Once you have identified these restrictions, the domain is all real numbers except for the values that are restricted.
Some common types of functions with restricted domains include rational functions, square root functions, and logarithmic functions. These functions have restrictions on the input values due to the nature of their equations.
Yes, a function can have an infinite domain. This means that there are no restrictions on the input values and the function is defined for all real numbers.
To sketch the domain of a function on a graph, you can use a number line to represent the input values. Any values that are restricted should be marked as open circles to indicate that they are not included in the domain. The remaining values should be connected with a line to show that they are included in the domain.