Understanding the Range in Mathematics: Methods for Finding the Set of Possible Values of a Function

range

In mathematics, the range refers to the set of all possible values that a function or relation can output

In mathematics, the range refers to the set of all possible values that a function or relation can output. It represents the variation in the dependent variable or the outputs of a function. The range could be a set of numbers, a range of values, or even an interval, depending on the context.

To find the range of a function, you need to consider all the possible values that the function can take on. Here are two common methods to find the range:

1. Algebraic method (for functions defined algebraically):
– Start by finding the expression for the function or equation.
– Next, simplify the expression as much as possible.
– Finally, determine the range of the simplified expression by identifying the set of possible output values.

2. Graphical method (for functions represented graphically):
– Plot the graph of the function.
– Identify the highest and lowest points on the graph vertically.
– The range is then determined by the set of all possible y or output values.

It is important to note that in some cases, a function may have a specific domain, which can limit the range of possible outputs. Additionally, certain functions may have an infinite or undefined range.

For example, let’s consider the function f(x) = x^2. In algebraic terms, we can describe this function as y = x^2. On the graph, when you plot different values of x, you can observe that the function outputs positive values for all real numbers, and never outputs negative values. In this case, the range would be all non-negative real numbers, which can be represented as [0, +∞).

Overall, finding the range of a function involves understanding its inputs and outputs, either algebraically or graphically, and determining the possible values that the function can generate.

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