Func

MAT1108 Foundations of Mathematics Lecture 6 Summary commemorates Semester 1, 2012 FUNCTIONS I 6.1 Functions: Definition, eminence and language Definition of a Function A bump is a befall out which takes certain weighs as inputs and assigns to individually input number exactly one proceeds number. The inputs and outputs argon alike called variables. In this unit, we shall assume that both inputs and outputs are factual numbers, and hence we shall hear only real- nurtured turn tails. A matter can be correspond by words, an equation (formula), a graph, or a accede of numbers. The notation = (), read equals of , is utilize to designate that is a process of . Thus, applying the rule to the input value, , gives the output value, (). In other words, () stand fors a value of . Here, is called the aquiline variable and is called the independent variable. Function Notation Note that we could hand over used any letter, not just f, to represent t he rule. Similarly, we could also use other letters to represent the variables. For example, = () or = (). input signal and Output Sometimes, our objective is to go on 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 particular value of the input. At other times, the situation is reversed. We know the output and we want to find the corresponding input. If the function is given by an equation, the input value are solutions to an equation. The process of finding input values is cognize as solving equations. EXERCISE 6.1 (a) (0) (b) (1) Suppose () = 1 ? + 2 2 , evaluate and simplify the following 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) Given tha! t () = 2 ? 3 + 5, evaluate...If you want to get a full essay, order it on our website: BestEssayCheap.com

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