Understanding Increasing Functions: Definition and Examples

increasing function

An increasing function is a concept in mathematics that describes a function whose output values (y-values) increase as the input values (x-values) increase

An increasing function is a concept in mathematics that describes a function whose output values (y-values) increase as the input values (x-values) increase.

More formally, let’s consider a function f(x). Suppose for any two real numbers x1 and x2, if x1 < x2, then f(x1) < f(x2). In this case, f(x) is said to be an increasing function. To understand this concept, let's look at a simple example. Consider the function f(x) = 2x. If we plug in different x-values, we can observe that the corresponding y-values will increase. For instance: f(1) = 2 * 1 = 2 f(2) = 2 * 2 = 4 f(3) = 2 * 3 = 6 As we can see, as x increases, the y-values also increase. Therefore, the function f(x) = 2x is an increasing function. Another example could be the function g(x) = x^2. By plugging in different x-values, we can observe that the resulting y-values also increase. For instance: g(1) = 1^2 = 1 g(2) = 2^2 = 4 g(3) = 3^2 = 9 Again, as x increases, the y-values increase as well. Hence, the function g(x) = x^2 is also an increasing function. It is important to note that this concept applies to functions defined over a certain domain. Some functions might be increasing in one domain but decreasing in another. Therefore, it is always necessary to specify the domain on which the function is increasing. In summary, an increasing function is a function where the output values increase as the input values increase. This behavior is observed by comparing the function's output values for different input values, and if the output values increase with increasing input values, the function is considered to be increasing.

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