Module+9+Functions

MODULE 9 FUNCTIONS Scheme of Work || Scheme of Work || || Core Assignment Module 9 || __ Types of function. Domain and Range. Symmetry, period, asymptotes, vertices, intercepts __ For a function f defined by an expression with variable x, the implied domain of f is the set of all real numbers variable x can take such that the expression defining the function is real. The domain can also be given explicitly. __**Definition of the Range of a Function**__ The range of f is the set of all values that the function takes when x takes values in the domain.
 * EXTENDED || CORE ||  ||
 * Can Do Statements
 * Extended Assignment Module 9
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 * * __**Definition of the Domain of a Function**__

> {(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)} ** The above list of points, being a relationship between certain // x //'s and certain // y //'s, is a relation. The domain is all the // x //-values, and the range is all the // y //-values. To give the domain and the range, I just list the values without duplication: ** domain: {2, 3, 4, 6} ** An **asymptote** of a real-valued function //y// = //f//(//x//) is a curve which describes the behavior of //f// as either //x// or //y// tends to infinity. || __ Transformations of functions __ __ Trigonometric functions and their transformations __ __ Using function notation, composite and inverse functions __ __ The log function __ __ The Log laws, solving Log equations __ Logs are very simmilar to indices, so the rules you use are basically the same. Logs take this basic format; Loga^x Here's the basic rules: Logb(zy)= logb(z) + logb(y) Multiplication inside the log is addition outside and vice versa. logb(z/y)= logb(z) - logb(y) Like multiplication, division inside the log is the same as subtraction outside it. Example: simplify log3 + log4 – log 2 Step 1: log3 +log4= log(3*4) = log12 Step 2: log12 – log2= log(12/2) = log6
 * ** State the domain and range of the following relation. Is the relation a function?
 * range: {–3, –1, 3, 6} **
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 * Logs are short for logarithims.

This one is very important for solving equations with powers! logb(zy)= y logb(z) How is this useful? Let's imagine you get a question where you need to solve an equation to find x; 5x= 2 To answer it, you use logs; This makes it But you have to put it on the otherside as well, to keep the equation balanced. ||