The graph is defined for all x between - 8 and 8. The graph starts at x = - 8 and ends x = 8. What is the domain of the graph of the function? Hence the domain, in interval notation, is written as There are points on the graph for all values of x between - 4 and 4 including at - 4 and 4. The graph starts at x = - 4 and ends x = 4. What is the domain, in interval notation, of the graph of the function shown below? Note that we close the brackets of the interval because -4 and 6 are included in the domain which is indicated by the closed circles at x = - 4 and x = 6. In inequality notation, the domain is written as For all x between -4 and 6, there points on the graph. The graph starts at x = - 4 and ends x = 6. With these ideas and definition, we will now solve examples where the whole domain of a given graph is found.ĭomain of a Graph Examples with Detailed Solutions Example 1įind the domain of the graph of the function shown below and write it in both interval and inequality notations.
These values and more other values of x are not included in the domain. There are no points on the graph at x = - 1 (open circle on the graph), 0.5, 1, 1.5, 2 (open circle). These values and more other values of x are included in the domain of f. Hence, For a function f defined by its graph, the implied domain of f is the set of all the real values x along the x-axis for which there is a point on the given graph.Īs an example there are points on the graph below at x = - 3, - 2.5, -2, -0.5, 2,5, 3, 3.2, 4. The graph of a function f is the set of all points (x, f(x)). The implied domain of a function f is the set of all values of x for which f(x) is defined and real.