How to find the exact formula of the function if the graph of it is given?

To begin with, answering this question requires basic knowledge of simple Mathematical function and ability to solve simultaneous equations. One thing you need to be able to do is recognising what kind of function is drawn in the sketch, for example, it could be hyperbola, parabola, straight line or something else. Besides that, you need to know general equations that represent these functions. For instance, the general equation for straight line is y = kx + b or that the equation for parabola is y = ax² + bx + c (different people might use different notations, but it looks more or less the same). After identifying the graph and general formula of it, next thing you need to do is take some points from the graph and insert it into the general equation. Amount of points that needs to be taken is the amount of unknowns in our general formula. Let us say that our straight line is y = kx + b, therefore there are two unknown variables: k and b (we know y and x visually from the graph). For example, let us say that from the graph we figured out that when x = 0, y = 1 and when x = 2, y = 5. Therefore, we take those values and plug into our general equation: 1st case: 1 = k * 0 + b; 2nd case: 5 = k * 2 + b. Here we get a pair of simultaneous equations. First equation can be simplified, because k * 0 = 0, therefore 1 = b, after than we can plug in this result into 2nd equation and get this: 5 = k * 2 + 1, from here we move all the numbers to the left side and we left with 2 = k, and now we plug in these values into our general equation to get the exact formula of the graph. Final answer: y = 2x + 1