The Concept of Increasing Functions | Understanding Function Behavior as Inputs Increase

Function is increasing

When we say that a function is increasing, it means that as the input values (or independent variable) of the function increase, the corresponding output values (or dependent variable) also increase

When we say that a function is increasing, it means that as the input values (or independent variable) of the function increase, the corresponding output values (or dependent variable) also increase. In other words, the function “goes up” as you move from left to right on its graph.

More formally, a function f(x) is increasing if for any two input values a and b, such that a < b, the corresponding output values f(a) and f(b) satisfy the inequality f(a) < f(b). This means that the function values are getting larger as the input values increase. For example, let's consider the function f(x) = 2x. As we substitute different positive input values, we can observe that the output values increase. Let's calculate a few values: f(1) = 2(1) = 2 f(2) = 2(2) = 4 f(3) = 2(3) = 6 We can clearly see that as the input values increase (1, 2, 3), the output values also increase (2, 4, 6). Therefore, we can say that this function is increasing. Graphically, an increasing function is represented by a rising curve on a coordinate plane. The slope of the curve is positive, indicating the upward movement. Keep in mind that a function can be increasing on a certain interval or for its entire domain.

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