Understanding Decreasing Relationships in Mathematics | Exploring Decreasing Functions and Sequences

Decreasing

In mathematics, “decreasing” is a term used to describe a pattern or trend where a quantity or value decreases as the input or independent variable increases

In mathematics, “decreasing” is a term used to describe a pattern or trend where a quantity or value decreases as the input or independent variable increases. It indicates a decreasing relationship between two variables.

More formally, we say that a function is decreasing if for every pair of inputs (x1 and x2) where x1 < x2, the corresponding outputs (f(x1) and f(x2)) satisfy the inequality f(x1) > f(x2). In other words, as the input values increase, the function’s output values decrease.

For example, consider the function f(x) = 3x – 2. This linear function is decreasing because as x increases, the output values (f(x)) decrease. If we evaluate the function for x = 1 and x = 2, we get f(1) = 1 and f(2) = 4. Since 1 < 2 and 1 > 4, we can see that f(x) is indeed decreasing.

The concept of decreasing can also be applied to sequences, where each term is less than or equal to the previous one. For instance, the sequence 10, 7, 4, 1 is a decreasing sequence as each term is smaller than the previous one.

In summary, when we say something is “decreasing” in mathematics, it means that as the input variable increases, the corresponding output values decrease, either in a function or a sequence.

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