The decreasing intervals of a function
The decreasing intervals of a function
A decreasing interval of a function expresses the same values of X (the interval), in which the values of the function (Y) decrease parallelly to the increase of the values of X to the right.
In certain cases, the decreasing interval begins at the maximum point, but it does not necessarily have to be this way.
Is the function in the graph decreasing?
Is the function shown in the graph below decreasing?
To solve this problem, we'll follow these steps:
Now, let's work through each step:
Step 1: Observing the graph, the function's graph is a line moving from the top left to the bottom right. This indicates it slopes downward as we move from left to right across the -axis.
Step 2: According to the definition of a decreasing function, for any , it must hold true that . Since the graph shows a line moving downward, this condition is satisfied throughout its domain.
Therefore, the function represented by the graph is indeed decreasing.
The final answer is Yes.
Yes
Is the function in the graph decreasing?
To analyze whether the function in the graph is decreasing, we must understand how the function's behavior is defined by its graph:
Therefore, the function represented by the graph is not decreasing.
No
In what domain is the function increasing?
Let's first remember that a function is increasing if both the X and Y values are increasing simultaneously.
Conversely, a function is decreasing if the X values are increasing while the Y values are decreasing simultaneously.
In the graph shown, we can see that the function is increasing in every domain and therefore the function is increasing for all values of X.
All values of
In what interval is the function increasing?
Purple line:
Let's remember that a function is described as increasing if both X values and Y values are increasing simultaneously.
A function is decreasing if X values are increasing while Y values are decreasing simultaneously.
In the graph, we can see that in the domain the function is increasing, meaning the Y values are increasing.
Determine in which domain the function is negative?
Remember that a function is increasing if both X values and Y values are increasing simultaneously.
A function is decreasing if X values are increasing while Y values are decreasing simultaneously.
In the graph, we can observe that in the domain the function is decreasing, meaning the Y values are decreasing.
Is the function in the graph below decreasing?
Is the function in the graph decreasing?
Does the function in the graph decrease throughout?