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Title of Lesson: Introduction to Functions Section: 1.2 Pages: 16-29 My Learning Goals 1. Functions – decide if a relation is a function. Use function notation and evaluate functions. Use functions to model applications 2. Find the Domain and Range of function and represent them using interval notation. 3. Evaluate difference quotients. Vocabulary/Formulas 1. Function – every input has one unique output. 2. Domain – The set of inputs for which the function is defined. 3. Range – The set of possible outputs for a given function 4. Piece-wise function – A function that is defined by two or more equation over a specific domain. 5. Difference Quotient- f (x + h) - f (x) ,h ¹ 0 h Prerequisite Skills with Practice 1. Evaluate the following function for f(3), f(0) and f(-3). f (x) = -x + 3x - 3 2 2. Isolate “y” in the follow equation. (x -2) +(y+ 3) = 25 2 2 Notes When is a relation a function? Tables: Vertical Line Test. Graphs: Notes Testing for functions algebraically. x + y =1 ± sign. x+ y =1 Looking for a 2 2 Notes Piecewise-Defined Function Evaluating. ì5 - 2x 2 , x < 0 Given f (x) = í î2x + 5, x ³ 0 Evaluate f(-2), f(0), f(3) Notes Piecewise-Defined Function Sketching. ì-2x +1,x < 2 f (x) = í î x + 3,x ³ 2 ì x +1, x < -3 ï g(x) = í2,-3 £ x £ 0 ï-x + 3, x > 0 î Notes Determining domains of functions. Need to consider the values for which the function is defined and the real world implications of the function. f : {(-3,0),(-1,4),(0,2),(2,2),(4,-1)} g(x)= -3x +4x+5 2 1 h(x) = x+5 4 3 The volume of a sphere: V = p r 3 k(x) = 4 - 3x Notes The box problem. Calculator Skills: • Basic Input • Adjusting Window • Finding Maximums A sheet of metal 12 inches by 10 inches is to be used to make a open box. Squares of equal sides x are cut out of each corner then the sides are folded to make the box. Find the value of x that makes the volume maximum. Notes Difference Quotients f (x + h)- f (x) ,h ¹ 0 h Understanding graphically and algebraically. Find the Difference Quotient for the functions below and simplify your answer. Homework Assignment: Pg. 23 1, (5-9) odd (13-24) all (27-41) odd (44-64) all 74,76,77, (87-90) all