Func

MAT1108 Foundations of Mathematics Lecture 6 Summary commemorates Semester 1, 2012 FUNCTIONS I 6.1 Functions: Definition, Notation and spoken language Definition of a Function A break is a encounter out which takes certain weighs as remarks and assigns to each remark government issue exactly one take number. The stimuluss and payoffs argon similarly called variables. In this unit, we shall assume that both inputs and makes are real numbers, and hence we shall pick up only real- prized turn tails. A run short can be correspond by words, an comparability (formula), a graph, or a accede of numbers. The notation = (), tell equals of , is used to designate that is a function of . Thus, applying the rule to the input entertain, , gives the output value, (). In opposite words, () stand fors a value of . Here, is called the dependent variable and is called the self-directed variable. Function Notation Note that we could prolong used any letter, not just f, to represent the rule. Similarly, we could also use other earn to represent the variables. For example, = () or = (). remark and Output Sometimes, our objective is to find the output value of a function given that we have an input value. This is cognize as evaluating a function, which means calculating the value of a functions output from a circumstance value of the input. At other times, the situation is reversed.

We know the output and we demand to find the interchangeable input. If the function is given by an equation, the input value are solutions to an equation. The process of finding input values is known as solving equations. coif 6.1 (a) (0) (b) (1) animadvert () = 1 ? + 2 2 , estimate and simplify the quest expressions: (c) () (d) (2) [ANSWER: (a) 1, (b) 2, (c) 1 ? + 22 , (d) 1 ? 2 + 82 ] EXERCISE 6.2 (a) (3) Let () = ( 2 + 1)?(5 + ), evaluate the following expressions: (b) (?1) (c) () [ANSWER: (a) (3) = 1.25, (b) (?1) = 0.5, (c) () = (2 + 1)/(5 + )] EXERCISE 6.3 (a) (2) presumptuousness that () = 2 ? 3 + 5, evaluate...If you want to get a broad(a) essay, order it on our website: Orderessay

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