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 $Question from John, a student: I don't understand how to pick coordinates for y=f(x). I took a look at your answer to a previous question here: http://mathcentral.uregina.ca/QQ/database/QQ.09.00/monica2.html What does y= f(x) actually mean? when I think of y=f(x), i Think of y = f(x)= 1, x = 1, x =2, then y =f(x) =2, x =3, then y= f(x)=3, and so on. Hi John, I find it helps sometimes to think of a function as a machine, one where you give a number as input to the machine and receive a number as the output. The name of the function is$f,$the input is$x$and the output is$f(x),$read "$f$of$x".$The output$f(x)$is sometimes given an additional name$y$by$y = f(x).$The example that comes to mind is the square root function on your calculator. The name of the function is$\sqrt{\;\;}$and we usually write the function as$f(x) = \sqrt{x}.$On my calculator I input$x$for example by pressing 2 then 5. Then I invoke the function by pressing the$\sqrt{\;\;}$button I and receive 5 on the calculator display. Thus$\sqrt{25} = 5.$Let me look at another example,$y = f(x) = x^2 - 4.$In this example I am describing the function$f$by the way it operates. By$f(x) = x^2 - 4$I am telling you that if you input a number$x$to this function then the function squares$x,$subtracts 4 and returns the result. Thus for example if$x = 3$then$y = f(3) = 3^2 - 4 = 9 - 4 = 5.$To graph this function I would start by choosing some values of$x$and since I get to choose I would select values that make the arithmetic easy. For example$x = 0, x = 1, x = -1$and so on. I am going to keep track of what I am doing by using a table. x y = f(x) 0 -4 1 -3 -1 -3 2 0 3 5 Add a few more rows to the table choosing your own values of$x.$Plot the values in your table$(0, -4), (1, -3)\$ etc. on graph paper and then see if you can sketch a graph that goes through these points.

Write back if you need more help,
Penny

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