# 09.07 - For graphing problems you have to show work(e.g...

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For graphing problems, you have to show work (e.g., plot specific points). You won’t get much credit if it looks like you could have just copied your picture from the output of a graphing calculator. Key concepts of section 1.1: Function, domain, range Increasing, decreasing, even, odd [Have the students define these.] Function: A function f is a rule that associates values of y with values of x , so that each value of x is associated with at most one value of y . (Why “at most one value?” Differential calculus – the subject of 92.141 – is about how a change in one variable effects another variable. It’s best suited to situations in which the value of one variable, x , completely determines the value of another variable, y ; we call x and y the independent and dependent variables, respectively. Later we’ll see how the methods can be applied to situations where x does not completely determine y , as in the case of the circle x 2 + y 2 = 1 for instance.) Example: f ( x ) = 1 – 1/ x is a function of x (it has one value

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when x is non-zero, and no values when x is zero). Non-example: g ( x ) = ± sqrt( x ) is not a function of x (it has two values when x is positive). Domain: The
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09.07 - For graphing problems you have to show work(e.g...

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