1. FIRE UP! With your neighbor, simplify the following expression and be ready to share out ! Ready GO! (x + 3) 2 WEDNESDAY

2. Graphing Parent Functions and Functional Notation Chapter 1 Section 1-2,3,5

3. Objectives I can sketch parent function graphs using critical points I can find functional values of any function –From an equation –From a graph

4. Functions A function is a special relation in which each element from the domain is paired with exactly one element from the range.

5. Function A function is a correspondence between a first set, called the domain, and a second set, called the range, such that each member of the domain corresponds to exactly one member of the range. FunctionNot a Function  749  24 7 57 00 63  24 8 2

6. SOLUTION GUIDED PRACTICE for Example 2 Tell whether the pairing is a function. 1221 Output 12963 Input 2. 3 6 9 12 12211221 The pairing is a function because each input is paired with exactly one output.

7. Parent Functions These are the 8 parent functions for this unit!! –Constant –Linear –Quadratic –Cubic –Absolute Value –Square Root –Reciprocal –Greatest Integer

8. Critical Points You must graph all the critical points for each function! 10x10 Grid all year

9. Graph: f(x) = 0

10. Linear What are critical points Xy 00 11 22 -2 33 -3

11. Graph: f(x) = x

12. Quadratic What are critical points Xy 00 11 1 24 -24 39 -39

13. Graph: f(x) = x 2

14. Graph: f(x) =

15. Square Root What are critical points Xy 00 11 42 93 164

16. Graph: f(x) =

17. Functional Notation Functional notation is a way to express an equation as a function If we have an equation y = 2x + 3 We can write this in functional notation as: f(x) = 2x + 3 f(x) replaces the y It is read “f of x” x is the input and f(x) is the output

18. Finding a Functional value f(x) = 6x + 10 Find f(-3) This means substitute –3 for all x variables and evaluate f(-3) = 6(-3) + 10 = -18 + 10 = -8 g(x) = 2x 2 + 4x – 1 Find g(-3) g(-3) = 2(-3) 2 + 4(-3) – 1 2(9) + (– 12) – 1 18 – 12 – 1 5

19. What does this mean? f(3) This reads as “ f of 3” Simply put: “What is the y-value for an x-input of 3

20. SOLUTION EXAMPLE 5 Evaluate functions Evaluate the function when x = – 4. a. f (x) = – x 2 – 2x + 7 Write function. f (– 4) = –(– 4) 2 – 2(– 4) + 7 Substitute –4 for x. = –1= –1 Simplify.

21. Practice Problem Given f(x) = x 2 + 2x – 1, find f(2). Practice Problem Given f(x) = x 2 + 2x – 1, find f(–3). f(2) = (2) 2 +2(2) – 1 = 4 + 4 – 1 = 7 f(–3) = (–3) 2 +2(–3) – 1 = 9 – 6 – 1 = 2 Evaluate f(@). Given f(x) = x 2 + 2x – 1 f(@) = (@) 2 + 2(@) – 1 = @ 2 + 2@ – 1. Given that f(x) = 3x 2 + 2x, find f(h). f(h) = 3(h) 2 + 2(h) = 3h 2 + 2h

22. From a Graph You can also pick functional values from a graph Remember f(x) replaced “y” So, you are just finding y-values corresponding to the x-values

25. Step It Up Find f(x + 2)

26. Homework WS 1-2 Signed Paperwork and Supplies if you forgot Work on Parent Function Packets