Decreasing Function
Let f be a function defined on an interval I and let x₁ and x₂ be any two points in I. F decreases on I if x₁ < x₂ → f(x₁) < f(x₂).
A decreasing function is a type of function in mathematics in which the output value decreases as the input value increases. In simpler terms, it means that as you move from left to right on a graph of a decreasing function, the corresponding y-values get smaller.
There are different ways to define a decreasing function. However, the most common way is to say that a function f(x) is decreasing on an interval I if for any two points a and b in I with a
In other words, if the value of the function at point a is greater than the value of the function at point b, then the function is decreasing on the interval I.
A common example of a decreasing function is the exponential decay function, which is given by the equation:
y = a(1-r)^x
Where a is the initial value, r is the rate of decay, and x is the independent variable (input value). As x increases, the value of y decreases, and this can be seen on a graph of the function as a downward slope to the right.
Other examples of decreasing functions include trigonometric functions such as cosine and tangent, as well as polynomial functions where the coefficient of the highest degree term is negative.
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