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FUNCTIONS!

A function is a set of data that has a single output for each input. Functions describe the relationship between an input and its output.

Now that is something very difficult to understand so lets just try to make that more simple.

Lets say you had a graph for y=x it would be something like.......

lets take this graph and lets take the definition we wrote when we began this chapter lets link up the two.

you will find that for the equation y=x we need to substitute a value for x to get a value for y to get a set of co ordinates so that we can plot it on a graph. similarly we can do the opposite we can use a value of y to get a value for the x axis.

focus that you need to put something into the equation to get something out of the equation hence an input to get an output.

in terms of functions this input is a domain. in our daily lives we consider the domain to be an area a person is supposed to work in for example a doctor has his hospital and etc hence not only is the doctor supposed to work for the hospital but hes valuable to it as well. similarly while sketching a graph a domain is very important because not only does it define the output but also limits the area of the graph.

lets make this more simple lets use a graph for -1<x<1

fixing the domain to abide by certain values you get a graph that does not cross a certain area/value for x.

in this manner when we talk about the output the output is basically the coordinates of y with respect to the input. for the above graph the output is from -1 to 1. the output is also called as the range the range at which the graph is spread out speaking in terms of the y axis.

to sum it up domain consists of the value of x axis and range is the values for the y axis (input and output)

talking about functions when we represent the domain we represent it with x and we represent it with f(x)

similarly when we write y=x it is actually f(x)=x.

there are certain things about functions that we are supposed to know like what are one one functions what is an inverse of a function and etc.

how ever we are gonna talk a bit more about functions. lets talk about what linear functions are

linear functions are functions to which if we draw a graph it would result in a straight line like the one above. a linear function is basically the most easiest function XD.

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