Function comes in all shapes and sizes. It means that every function is different than others. It also means that their graph will also be different. To make things easier, let's understand that we have divided the graphs into two types. One is the increasing function and another is the decreasing function. As the words tell you, increasing function means that their graphs are increasing, on the other hand, decreasing function means that their graphs are decreasing but at what rate? In this lesson, you will learn everything about increasing and decreasing functions.

Strictly Increasing Function

If the graph of the function is increasing at an increasing rate that means you have a strictly increasing function. There are two identifications of this graph, the first one is the curve going upwards. It means that the gradient (slope) of the graph will increase as you increase the value of x. The second identification is the big change in f (x). When you find the change (meaning difference of previous value from the next value), you will see that the change is increasing. These both indicate that you are dealing with a function that is increasing strictly.

x > a \Rightarrow f(x) > f(a)

x < a \Rightarrow f(x) < f(a)

 

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Increasing Function

When you are dealing with an increasing function graph, you will notice one thing different and that is the graph is steeper than the strictly increasing function. It means that sometimes there will be no change but then after a few values of x, there will be a sudden change. Although, one thing is for sure and that is the graph is increasing.

x > a \Rightarrow f(x) \geq f(a)

x < a \Rightarrow f(x) \leq f(a)

 

Strictly Decreasing Function

You might have some idea for this function after reading the strictly increasing function. If the function value is decreasing for ascending values of x that means the function is decreasing function. The point to notice is that for every ascending value of x, the value of the function is decreasing. That is the most important point for strictly decreasing function. The gradient of the graph will also decrease for every new value of x and not to mention that the shape of the graph will be a descending curve for increasing values of x.

x > a \Rightarrow f(x) < f(a)

x < a \Rightarrow f(x) > f(a)

 

Decreasing Function

Last but not least, for decreasing function, there are two parts, the first part is that there will be a constant decrease in function. We can say a linear decrease in the function for ascending values of x. The second part is the part where all the values of function will remain constant for ascending values of x.

x > a \Rightarrow f(x) \leq f(a)

x < a \Rightarrow f(x) \geq f(a)

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.