A function is decreasing when…
A function is considered decreasing when its values decrease as the input variable increases
A function is considered decreasing when its values decrease as the input variable increases. In simpler terms, this means that as the x-values increase, the corresponding y-values decrease.
To determine if a function is decreasing, you can follow these steps:
1. Identify the function: Look at the given equation or polynomial expression and determine the function in question. For example, let’s consider the function f(x).
2. Choose any two values: Select two different x-values, let’s say x1 and x2, where x1 < x2. These values will help us compare the y-values. 3. Evaluate the function: Substitute the x-values into the function and find the corresponding y-values. Calculate f(x1) and f(x2). 4. Compare the y-values: Compare the calculated y-values. If f(x1) > f(x2), then the function is decreasing. This means that as x increases from x1 to x2, the corresponding y-values decrease.
5. Repeat: You can repeat this process for different pairs of x-values to confirm if the function is consistently decreasing over its entire domain.
It’s worth mentioning that for some functions, determining whether it is increasing or decreasing can be more challenging, especially if the function is not given explicitly but rather as a graph or a table of values. In such cases, you can observe the trends in the graph or the table to identify any patterns of decreasing or increasing values.
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