Understanding Strictly Decreasing Functions: Definition, Examples, and Analysis

strictly decreasing

In mathematics, a function is said to be strictly decreasing if for any two numbers in its domain, the value of the function at the first number is strictly greater than the value of the function at the second number

In mathematics, a function is said to be strictly decreasing if for any two numbers in its domain, the value of the function at the first number is strictly greater than the value of the function at the second number.

To understand this concept better, let’s consider an example. Suppose we have a function f(x) = 3x – 2. We can check whether this function is strictly decreasing by comparing the values of the function at different points.

Let’s pick two numbers, say x = 1 and x = 2. Plugging these values into the function, we get f(1) = 3(1) – 2 = 1 and f(2) = 3(2) – 2 = 4. Since 4 is greater than 1, we can see that the function is not strictly decreasing.

Now, let’s choose another example. Consider the function g(x) = -2x + 5. Let’s compare the values of the function at two different points, x = 2 and x = 4. Plugging these values into the function, we get g(2) = -2(2) + 5 = 1 and g(4) = -2(4) + 5 = -3. Since -3 is less than 1, we can see that the function is strictly decreasing.

To summarize, a function is strictly decreasing if the value of the function decreases as the input variable increases. We can determine this by comparing the values of the function at different points. If the value of the function at the first point is strictly greater than the value of the function at the second point, then the function is strictly decreasing.

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