Strictly decreasing function definitions
| Word backwards | yltcirts gnisaerced noitcnuf |
|---|---|
| Part of speech | The part of speech of the phrase "strictly decreasing function" is a noun phrase. |
| Syllabic division | strict-ly de-creas-ing func-tion |
| Plural | The plural of strictly decreasing function is strictly decreasing functions. |
| Total letters | 26 |
| Vogais (5) | i,e,a,u,o |
| Consonants (10) | s,t,r,c,l,y,d,n,g,f |
A strictly decreasing function is a type of mathematical function that exhibits a consistent pattern of decreasing values as the input values increase. In other words, as the independent variable increases, the dependent variable decreases in a strictly monotonous manner without any fluctuations or plateaus.
Characteristics of a Strictly Decreasing Function
In a strictly decreasing function, the slope or rate of change is always negative. This means that the function is always decreasing and never increases as the input values change. Mathematically, this can be represented as f(x1) < f(x2) if x1 > x2 for all x1 and x2 in the domain of the function.
Graphical Representation
Visually, a strictly decreasing function appears as a curve that consistently slopes downwards from left to right on a graph. The curve never levels off or turns upwards, demonstrating a clear downward trend throughout its domain.
Examples of Strictly Decreasing Functions
Examples of strictly decreasing functions include exponential decay functions, such as y = e^(-x), where the value of y decreases exponentially as x increases. Another example is the function f(x) = -2x, where the slope is constantly negative, leading to a strictly decreasing function.
In conclusion, a strictly decreasing function follows a predictable pattern of decreasing values as the input values increase. Understanding this type of function is crucial in various mathematical and scientific contexts where trends need to be analyzed and predicted accurately.
Strictly decreasing function Examples
- The graph of the cubic function y = x^3 is a strictly decreasing function in the interval (-∞, 0).
- A function f(x) = -2x - 5 is a strictly decreasing function for all real numbers x.
- In mathematics, a strictly decreasing function is one that always decreases as x increases.
- The exponential function y = 2^-x is a strictly decreasing function for x > 0.
- A polynomial function of degree 4 with all negative coefficients is a strictly decreasing function.
- The function f(x) = -|x| is a strictly decreasing function for x < 0.
- The square root function y = √x is a strictly decreasing function on the interval (0, ∞).
- A logarithmic function y = log(x) is a strictly decreasing function for x > 1.
- A rational function with a negative leading coefficient is a strictly decreasing function for x > 0.
- A trigonometric function such as y = sin(x) is a strictly decreasing function on certain intervals.