Question

What are the steps for finding a function rule, if you are given the graph of a function?

Answer 1

If the graph of function is not given,and then it has been asked to find the function rule, it will be tedious task.The reason is that , there are many kind of functions

1.Linear Function---- (Graph will be a Straight line)

2.Logarithmic Function

3.Exponential Function , either in the form of ,

$e^x \text{or} a^x$

I have drawn the graph of these three kind of function.If the function is linear, take any two points on the line then use Two point form of equation of line to find the function rule.Suppose two points on the line are

$(x_{1},y_{1}),\text{and},(x_{2},y_{2})$

Now, Two point form of equation of line is,

$\rightarrow\frac{y-y_{1}}{x-x_{1}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

There are many more kind of functions, like parabola , Ellipse, Hyperbola function , if few parameters are given then you can find equation of these function.

Answer 2

First of all you need to find the coordinates of each points in the graph. Second is to find the slope or the rise over run of the graph when it is connected to every points. The third is to apply the formula in solving the function by assigning each value. The formula is Y=MX+B