## range of a function

### The range of a function refers to the set of all output values or the collection of all possible y-values that the function can produce

The range of a function refers to the set of all output values or the collection of all possible y-values that the function can produce. In other words, it represents the complete set of values that the function can take on.

To find the range of a function, you need to examine the set of all output values that the function generates for every possible input value in its domain.

Here are a few methods to determine the range of a function:

1. Analyzing the graph: If the function is represented by a graph, you can look at the vertical extent of the graph. The range will be the collection of all y-values covered by the graph. For example, if the graph extends from y = -2 to y = 4, then the range of the function is [-2,4].

2. Observing the equation: If the function is given by an equation, you can analyze the equation to determine the potential range of values. For instance, if the equation is y = x^2, it represents a parabola that opens upward and has a vertex at (0,0). Therefore, the lowest y-value it can produce is 0. Thus, the range of this function is [0,∞).

3. Applying mathematical reasoning: For some functions, you can analyze the behavior of the function without a graph or an equation. For example, if you have a linear function like y = 2x + 3, you can observe that as x increases or decreases, y will also change in a similar manner. Hence, the range of this function is (-∞,∞).

4. Using calculus techniques: If you are dealing with a continuous function and have knowledge of calculus, you can take the derivative of the function and find its critical points. By evaluating the function at these critical points and examining its behavior on either side, you can determine the range of the function.

Remember that the range of a function depends on its domain. Some functions may have specific restrictions on the values they can take on, which could limit the range.

It is crucial to carefully consider the function’s behavior, graph, and equation, if applicable, in order to determine its range accurately.

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