Question
Identify the intervals in which the function is decreasing.
- 1 and 3
- 2 and 5
- 2 and 4
- 3 and 5
Hint:
We need to find the function is decreasing interval in graph the slope of the function would be negative.
The correct answer is: 3 and 5
Here we have to find out the decreasing intervals.
Firstly, we must look the graph that how many intervals are given,
In this graph, There are total 5 interval were given .
For decreasing interval , the line must be downward line.
If we can see each interval,
In (1) interval the line going upward while moving towards left to right, then it is increasing interval.
In (2) interval the line going horizontally while moving towards left to right, then it is constant interval.
In (3) interval the line going downward while moving towards left to right, then it is decreasing interval.
In (4) interval the line going horizontally while moving toward left to right, then it is constant interval.
In (5) interval the line going downward while moving toward left to right, then it is decreasing interval.
Hence, the given intervals having 2 interval which function is decreasing which is (3 & 5).
The correct answer is 3 & 5 (option (d)).
For finding the decreasing functions in interval you must consider the given interval will be going downward from left to right .
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Let us consider a function that defined as 
then, the representation may exist as shown below.
Hence, Every object x that belongs to the set of inputs has exactly one object y that belongs to the set of outputs.
*** Hence, the technical definition of the function is a relation from a set of i9nputs to set of possible outputs where each input is related to exactly one output.
What is the definition of function?
Let us consider a function that defined as then, the representation may exist as shown below.
Hence, Every object x that belongs to the set of inputs has exactly one object y that belongs to the set of outputs.
*** Hence, the technical definition of the function is a relation from a set of i9nputs to set of possible outputs where each input is related to exactly one output.
