How do you graph functions? explain step by step.

A function is a mean to establish pairs: the function is a rule that tells you how to associate inputs and outputs.

We draw the inputs on the x axis, and the outputs on the y axis.

For every x value that you choose, the function will tell you which y value you should associate: y = f(x).

Now, in order to graph a function, you should draw "all" the points (x,y), where y = f(x).

This is clearly impossible (most of the time at least), because there are infinitely many of such points.

So, you usually have knowledge about the general behaviour of the function, and you only sketch some fundamental points, and "guess" the rest of the graph.

For example, if you have to graph a polynomial with degree 1, you should know that it is a line, and so you sample two points and you connect them: this is the easiest graph to draw (and the most accurate!)

If you have to draw a polynomial with degree 2, you should know that it is a parabola. So, you surely want to draw the vertex, and probably the axis of symmetry as well. Then, you may sample some extra point, but you'll have to approximate your graph, sooner or later.

x is the number of plates which costs $5 and y is the number of $10 plates.

the equation: 5x + 10y = 900 and y=2x

by solving these two equations, x=36 and y= 72, so the total number of plates is 108