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# Graphs of Composite Functions

TopIf we combine two functions and then combined two functions such that we follow the first function and get the answer. The answer we got is used in second function is known as composite function.
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 << 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.