Lesson+Plan+2+(1pg+1)

Class: Precalculus Section 1.4 (pt 2) Date: 24 Oct 2008 Learning Experience: //Introduction// – The students recently learned how to combine functions through basic arithmetic and composition. This lesson will build on that and expand to relations. For a warm up the students will answer the following: Is // x // ² + //y//² = 4 a function? Why or why not? Solve this for //y//.
 * Lesson 2 **

//Discovery activity/Questions// – After reviewing the previous day’s even numbered exercises, lead the class in a discussion on the following. ·  Does the system that we had for warm up follow a rule or pattern? ·  Was it a function? Since it wasn’t a function, what was it? ·  How can we tell if a rule is a function? //Class work// – The class will be lead to the notion of relations. Define __ Relation __ as any general rule that associates //x// and //y//. Given the relation // x // ² // y // + //y//² = 5, which of the following points are solutions? (2, -5) (1, 3)  (2, 1) The above example is what is called an “implicit relation” or a relation where the //x// and the //y// are on the same side of the equation. Relations that are solved for one of the variables are said to be “explicit relations.” Which of the following relations are implicit and which are explicit? //y// = -2//x// + 3 2//x// + //y// = 3 //x//² + //y//² = 49 //y// = ± √ (49 – //x//²)

Describe the graph of the relations // x // ² + 2//xy// + //y//² = 1 and | //y// | = //x// – 5. These will resolve to a set of parallel lines of m=1 and a sideways absolute value relation. //Homework// – Page 125 # 35 – 44, 50.