How to find domain and range of a graph

Have you ever stared at a graph and wondered where its boundaries lie? Perhaps you’re working on a math assignment or preparing for an exam, and you’re tasked with determining the domain and range of a function depicted in a graph. This can feel overwhelming, especially if you’re not sure how to identify the essential values that define the graph’s behavior. In this post, we will break down the process into simple steps to help you confidently find the domain and range of any graph.

To find the domain of a graph, identify all the possible x-values (inputs) and for the range, pinpoint all the possible y-values (outputs) that the graph can take.

Finding the domain and range of a graph involves a few systematic steps. First, let’s tackle the domain. The domain consists of all the x-values for which the function is defined. To find it, observe the graph from left to right and identify any breaks or restrictions. For example, if the graph has vertical asymptotes or holes where a function is undefined, those x-values should be excluded from the domain. If the graph is continuous without any interruptions, the domain may cover all real numbers.

Next, you’ll want to establish the range. The range consists of all the y-values that the function achieves. Look at the graph from bottom to top and note the lowest point and the highest point that the graph reaches. Just like with the domain, if there are any horizontal asymptotes or values that the graph never touches, these must be taken into account when defining the range.

In summary, both the domain and range are typically expressed in interval notation, using brackets for included values and parentheses for excluded values. By carefully observing the x-values and y-values on the graph, you can accurately pinpoint both the domain and range.