How do you read the graph of a function?

Question

I can interpret functions in the formula form but I simply can’t understand how it can become a graph. How would you transform one into the other?

In: 46

Answer 1

On a basic level a function (lets call it f) takes an input (lets call it i) and gives you an output (lets call that o).

A function only takes certain inputs, so lets put all of these allowed inputs into a set (lets call that set X).

Now we can put each individual i out of our set X into the function f and we reciev a certain output in relation to our input, so lets call this output o_i (i in reference to the input i)((so if we put in a differen i from our set x (lets call it j) we would get the output o_j)).

Now we can write this: f(i)=o_i

Now we can describe a graph in simple terms:

A graph is a set which contains tupels of the form (i,o_i).

This set (=graph) of our function f contains all possible touples regarding each element in X.

In a more math-like notation:

f: X -> f(X) and
Graph of f: {(i,f(i)}