1. Where is the vertex of this graph?

2. Domain & Range Know what the “domain” of a function is. Know what the “range” of a function is. Understand how to describe the domain and range of functions and the meaning of notation like x є R 2<x<8 Be able to explain how the range and domains of functions can be limited and give examples.

3. Functions What is a function, and what does it do?

4. Functions What is a function, and what does it do? Functions are like machines, you put a input in, and you get a output. is a image of x Notation:

5. Functions Functions are sometimes called mappings. It maps x values to an output.

6. Domain & Range Sometimes functions have restrictions. To fully describe a function, you need to define its domain and range. The domain of a function is given by the set values of x or inputs ℝ ℝ means real numbers

7. What is the Domain? Domain: xєlR -5≤x<7

8. What is the Domain? Domain: xєlR:-1<x≤1

9. What is the Domain? Domain: xєlR -5<x<-3

10. What is the Domain? Domain: xєlR -6≤x≤6

11. What is the Domain? Domain: xєlR -1≤x<11

12. Infinite Domains Domain: xєlR:x≥-5

13. Infinite Domains Domain: xєlR:x>2

14. Infinite Domains Domain: xєlR (x can take any value)

15. Function Domains Domain: xєlR x≥0 Even roots cannot be done on negative numbers

16. Function Domains Domain: xєlR x≠0 You cannot divide by 0 (note also that the output cannot be 0 you’ll need this later so don’t forget)

17. Domain Round Up The domain of a function is a description of the values of x for which it is to be defined. There are various reasons that a function may only take limited values. – It may be impossible to evaluate the function for particular values of x. – It may be that we are only interested in certain values (e.g. If the value of x represents time it cannot be negative)

18. Range of f(x) = x 2 is Domain & Range Range of a function is the set values given by If y = f(x), then the range is given by y-values Range of f(x) = x 2 is Domain – set x values, Range – set y values Alphabetically D is before R, and X is before Y,y ϵ ℝ

19. What is the Range? Range: yєlR 0≤y<25

20. What is the Range? Range: yєlR -2≤y≤2

21. What is the Range? Range: yєlR y> 1 / 5

22. What is the Range? Range: yєlR y≥3 All quadratics have a range that is greater or equal to their minimum y value (or less than or equal to their maximum for –ax 2 )

23. Range Round Up The range of a function is a description of the values of y (outputs) for which it is defined. There are various reasons that a function output may only take limited values. – It may be impossible to have particular values come out e.g.² will never be negative. – It may be that we are only interested in certain values of x therefore limiting how many come out. Domain – set x values, Range – set y values Alphabetically D is before R, and X is before Y

24. Domain & Range Domain – X values Range – Y values

25. Domain & Range The domain of the kraang is in Dimension-X Domain = x values

26. Domain & Range of Quadratics Quadratics will have a range above their vertex x ℝ Domain Range,y ϵ ℝ

27. Domain Range Domain & Range of Sqrt ℝ,f(x) ϵ ℝ Can’t take sqrt of negative numbers (we want real numbers as answer)

28. Domain Range Domain & Range of 1/x ℝ,f(x) ϵ ℝ

29. Match up Cards!

30. Some Things To Think On You have two minutes... What is the domain of possible x values for these functions... xєlR x≠0 and x≠ 3 xєlR x ≥ 3 / 5 2 mins!!! 1 min!!!

31. What Is The Domain and Range of… (3 minutes from my click) Domain xЄR Min point (2, -9) Range yЄR and y ≥ -9 Domain xЄR x≠3 Range yЄR and y≠0 Output can never be 0 (told you would need it later)

32. xЄR 0≤y≤2 (sinx between -1 and 1) yЄR 0≤x≤4 xЄR 0≤y≤2 (roots of numbers from 0 to 4) yЄR 0<x<2 xЄR y>1 yЄR Sketch & Find Domain & Range

33. Independent Study Exercise C page 13 Numerical Methods Test is next lesson Friday Collecting Homework next lesson as well