Determine The Range of The Following Graph Calculator

What is the Range of a Graph?

The range of a graph refers to the set of all possible output values (y-values) that a function or set of points can produce. For a function, the range is all the y-values that correspond to the domain (all possible x-values).

For example, if you have a set of points (2,3), (4,5), and (6,7), the range would be {3, 5, 7} because these are all the y-values in the set.

How to Find the Range of a Graph

Finding the range of a graph involves identifying all the y-values in the graph. Here's a step-by-step method:

1. Identify all the points or functions on the graph.
2. List all the y-values from these points or functions.
3. If the graph represents a function, determine the minimum and maximum y-values.
4. For continuous functions, consider the behavior at the boundaries and any critical points.

For functions, you can also use calculus to find the range by analyzing the function's behavior.

Examples of Finding Range

Example 1: Set of Points

Given the points (1,2), (3,4), and (5,6), the range is {2, 4, 6}.

Example 2: Function

For the function f(x) = x², the range is all non-negative real numbers [0, ∞).

Example 3: Graph with Boundaries

If a graph shows a parabola opening upwards with vertex at (0,1), the range is [1, ∞).

Common Mistakes When Finding Range

When determining the range, it's easy to make these mistakes:

• Forgetting to include all y-values in the set.
• Misidentifying the minimum or maximum values.
• Assuming the range is the same as the domain.
• Overlooking the behavior of the function at the boundaries.