1. 1.2: Functions and Graphs

2. Relation- for each x value, there can be any y-values. Doesn’t pass the VLT. (ex. (1,2), (2,4), (1,-3) Function- For each x-value, there can be only ONE y-value. Passes the VLT

3. (x) Domain- the independent value (y) Range – the dependent value State the domain and range using interval notation

4. 1) Identify the Domain and Range of Write answers in interval notation 2) Identify the Domain of 3) Identify the Domain and Range of 4) Identify the Domain and Range of 5) Identify the Domain and Range of

5. Basic types of Transformations: (c>0) Y=f(x) Horizontal shift c units right y= f(x-c) -- -- - - - - - - - - c units left y = f(x+c) Vertical shift c units up y = f(x) + c -- - - - - - -- - c units down y = f(x) – c Reflection (around x-axis) y= -f(x) Reflection (around y-axis) y= f(-x) Reflection (around origin) y= -f(-x)

6. Even Function: its graph is symmetric with respect to the y-axis Y= f(x) is even if f(-x)= f(x) Ex. Odd Functions: Its graph is symmetric with respect to the origin y= f(x) is odd if f(-x) = -f(x) Symmetric means EQUAL AREA ex. SO its ODD

7. EVEN ODD

8. You should know some basic graphs, so then you can apply transformations without a calculator p. 13 in the book

9. Piecewise Functions: a function in different formulas for different parts of the domain We should be able to know what it looks like from its equation Sketch this graph

10. Write the absolute value function as a piecewise function Write the absolute value function as a piecewise function

11. Composition of functions:

12. Homework: p.17 (1-18, 19-27 odd, 29, 31, 32, 34,38-48 even, 49,59-64, 65 a-b, Problem set # 66