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To find the domain of a function on a graph, identify the x-values that the graph covers, considering any restrictions or discontinuities.Understanding Domain
The domain of a function refers to the set of all possible input values (x-values) that the function can accept without causing any mathematical issues, such as division by zero or taking the square root of a negative number. When looking at a graph, the domain is represented by the horizontal extent of the graph along the x-axis.Steps to Find the Domain from a Graph
- Observe the Graph: Look at the graph and determine the leftmost and rightmost points where the graph exists. This will give you the range of x-values that are included in the domain.
- Identify Restrictions: Check for any breaks, holes, or vertical asymptotes in the graph. These indicate x-values that are not included in the domain. For example, if the graph has a hole at \(x = 2\), then \(2\) is not part of the domain.
- Use Interval Notation: Once you have identified the x-values that are included in the domain, express the domain using interval notation. For example:
- If the graph extends from \(x = -3\) to \(x = 5\) without any breaks, the domain is \([-3, 5]\).
- If there is a hole at \(x = 2\), the domain would be expressed as \([-3, 2) \cup (2, 5]\).
- Consider Infinite Extents: If the graph continues indefinitely in one or both directions, use infinity in your interval notation. For example, if the graph extends to the left without bound and to the right up to \(x = 4\), the domain would be \((-\infty, 4]\).
Examples
- For a linear function that extends infinitely in both directions, the domain is all real numbers, expressed as \((-\infty, \infty)\).
Mashup MathHow to Find Domain and Range of a Graph—Step-by-Step - Mashup MathNow, let’s do a quick review of some important vocabulary terms and concepts that you will need to be familiar with in order to learn how to find the domain and range of a graph. F…https://www.mashupmath.com › blog › how-to-find-domain-and-range-of-a-graphapluscalculus.comHow to Find Domain of A Function? [Step-by-step]Knowing how to find domain of a function is an essential skill in mathematics. It helps you avoid errors and understand where the function is defined. Why is it important to know h…https://apluscalculus.com › blog › how-to-find-domain-of-a-functionLumen LearningDetermine Domain and Range from a Graph | College Algebra - Lumen LearningGive the domain and range of the toolkit functions. Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible i…https://courses.lumenlearning.com › waymakercollegealgebra › chapter › find-domain-and-range-from-a-graph
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