For example: If we have three functions f: a → b and g: b → c.

This function acquired by putting the output of ‘g’ when it has an argument value of f (b) instead of ‘b’. If ‘c’ is a function ‘g’ of ‘b’ and ‘b’ is a function ‘f’ of ‘a’ then ‘z’ is the function of ‘a’ and we know that the composite function is always associative function.

Let’s discuss about Graphs of Composite Functions:To graph composite function we need to follow one example so it is more clear that how to draw the graph of composite function.

Example: Given f (a) and g (a) as shown in the graphs below, find (g o f) (a) for integral values of ‘a’ on the interval –3

__<__a

__<__3.

All the values of (g o f) (a) = g (f (a)) for a = –3, –2, –1, 0, 1, 2, and 3. So I'll just follow the points on the graphs and put all the values:

⇨(g o f) (–3) = g(f (-3)) = g(1) = –1;

I got the answer see at a = –3 on the f (a) graph, finding the corresponding b-value of 1on the f(a) graph, now see at a = –3 on the f (a) graph, found that this directed to b = 1, went to a = 1 on the g(a) graph, and found that this directed to b = –1. Similarly:

⇨(g o f )(–2) = g( f(–2)) = g(–1) = 3

⇨(g o f )(–1) = g( f(–1)) = g(–3) = –2

⇨ (g o f )(0) = g( f(0)) = g(–2) = 0

⇨ (g o f )(1) = g( f(1)) = g(0) = 2

⇨(g o f )(2) = g( f(2)) = g(2) = –3

⇨(g o f )(3) = g( f(3)) = g(3) = 1;

This is how to find coordinate of a graph.