The decreasing intervals of a function
Master identifying decreasing intervals of functions with step-by-step practice problems. Learn where function values decrease as x increases through guided exercises.
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.
In which interval does the function decrease?
Red line: \( x=0.65 \)
In what domain does the function increase?
Let's remember that the function increases if the values and values increase simultaneously.
On the other hand, the function decreases if the values increase while the values decrease simultaneously.
In the given graph, we can see that the function increases in the domain where x > 0 ; in other words, where the values are increasing.
Answer:
x > 0
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 x > 1 the function is decreasing, meaning the Y values are decreasing.
Answer:
x > 1
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.
Answer:
All values of
In what domain does the function increase?
Let's remember that the function increases if the X values and Y values increase simultaneously.
On the other hand, the function decreases if the X values increase and the Y values decrease simultaneously.
In the given graph, we notice that the function increases in the domain where x < 0 , meaning the Y values are increasing.
Answer:
x<0
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 x < 0.6 the function is increasing, meaning the Y values are increasing.
Answer:
x<0.6