12 Basic Functions

1. 12 Basic Functions Hannah Kiiskila and Mitch Pronga

2. Introduction Video • http://www.youtube.com/watch?v=M87p94A1dL8

3. Intro

4. The 12 Basic Functions

5. Find the Domain https://www.youtube.com/watch?v=2tC36VPxCmw

6. Finding the Domain of a Function Ex. • Y=X is the equation for the first basic function This is the table for the first basic function The domain would be (- , ) This is because all the values of Y Will give out a real X value

7. Ex. 2 Y=[X] is the equation of this graph This is table for the second basic function. The domain would be (- , ) This is because all the values of Y Will give out a real X value

8. Find the Range • https://www.youtube.com/watch?v=4kCHuVrtbc4

9. Finding the Range of a Function Ex. • This is the graph of the function Y=x^2 • To find the range you need to look at the graph to see what values of y the graph reaches. • By looking at the graph, you should see that the graph reaches all positive values of y and 0, but not the negative values of y. • Because of this, the range for y=x^2 is [0, ), which shows that the graph will start at 0, and reach all positive values of y.

10. Ex. 2 • This is the graph of y=x^3 • By looking at the graph, you should see that the graph reaches all values of y. (negative, 0, and positive) • Because of this, the range of of y=x^3 is (- , ), which shows that the graph reaches all values of y.

11. Bounded Above • Bounded above means that there is a FIXED value which the function never rises above. • The Basic Logistic Function is bounded above at 1. • It does not have a single Y value that goes above 1.

12. Bounded Below • Bounded below means there is a FIXED value which the function never goes below. • The squaring function is bounded below at 0. • It never has a Y value that goes below 0.

13. Bounded • A function is said to be bounded when it is bounded above and below. • The sine graph never has a Y value that crosses 1 or -1 thus it is bounded above and below.

14. Quizlet Activity • http://quizlet.com/415738/scatter/ • Go tothe website above and click start game. • Match the function with its correct name. • Try it as many times as you would like and try and get the best score! • Good luck!

16. 1. What is this graphs name? • A. Squaring Function • B. Reciprocal Function • C. Square Root Function • D. Greatest Integer Function

17. 2. What is this graphs name? • A. Sine Function • B. Cubing Function • C. Exponential Growth Function • D. Basic Logistic Function

18. 3. What is the name of this graph? • A. Reciprocal Function • B. Sine Function • C. Natural Logarithmic Function • D. Greatest Integer Function

19. 4. What is this graphs name? • A. Greatest Integer Function • B. Cosine Function • C. Identity Function • D. Basic Logistic Function

20. 5. What is this graphs name? • A. Cubing Function • B. Reciprocal Function • C. Exponential Growth Function • D. Cosine Function

21. 6. How is this graph bounded? • A. Above • B. Below • C. Both • D. Neither

22. 7. How is this graph bounded? • A. Above • B. Below • C. Both • D. Neither

23. 8. What is the range of this graph? • A. (-1, 1) • B. (- , ) • C. [-1,1] • D. [- , ]

24. 9. What is the domain of this graph? • A. (- , ) • B. (0, ) • C. [- , ] • D. [- 0, )

25. 10. What is the name, range, and domain of this graph? • A. Identity Function, (- , ), (- , ) • B. Identity Function, (- , 0] [1, ), (- , ) • C. Identity Function, [- , ], [- , ] • D. Squaring Function, [- , ], [- , ]

26. Answer Key • 1. C • 2. D • 3. B • 4. A • 5. B • 6. B • 7. C • 8. C • 9. A • 10. A

27. Bibliography • Pictures • http://www.google.com/imgres?um=1&hl=en&tbo=d&biw=1366&bih=643&tbm=isch&tbnid=hyqviEhvtcrUBM:&imgrefurl=http://www.mathsisfun.com/sets/function-square.html&docid=4PMl1sKL0__VUM&imgurl=http://www.mathsisfun.com/sets/images/function-square.gif&w=220&h=192&ei=92n8UPpkj4jxBPvogMgF&zoom=1&iact=hc&vpx=467&vpy=178&dur=37&hovh=153&hovw=176&tx=95&ty=63&sig=108440193668009717289&page=1&tbnh=150&tbnw=173&start=0&ndsp=23&ved=1t:429,r:3,s:0,i:144 • http://www.google.com/imgres?um=1&hl=en&tbo=d&biw=1366&bih=643&tbm=isch&tbnid=FOwN5nVR9dqYgM:&imgrefurl=http://en.wikipedia.org/wiki/Logistic_function&docid=RfC7PJvfh9XjxM&imgurl=http://upload.wikimedia.org/wikipedia/commons/thumb/8/88/Logistic-curve.svg/320px-Logistic-curve.svg.png&w=320&h=213&ei=c2r8UImKAYr29gTT7IHwDw&zoom=1&iact=hc&vpx=184&vpy=138&dur=506&hovh=170&hovw=256&tx=107&ty=84&sig=108440193668009717289&page=1&tbnh=142&tbnw=213&start=0&ndsp=18&ved=1t:429,r:1,s:0,i:85 • http://www.google.com/imgres?um=1&hl=en&tbo=d&biw=1366&bih=643&tbm=isch&tbnid=hC4ZMS8wHSmuBM:&imgrefurl=http://onemathematicalcat.org/Math/Algebra_II_obj/basic_models.htm&docid=vl1ukCpWngVlnM&imgurl=http://onemathematicalcat.org/Math/Algebra_II_obj/Graphics/fct_sqrt.gif&w=371&h=297&ei=vWj8UKHsEYWo8gThoYGwCQ&zoom=1&iact=hc&vpx=2&vpy=161&dur=602&hovh=201&hovw=251&tx=54&ty=89&sig=108440193668009717289&page=1&tbnh=147&tbnw=184&start=0&ndsp=23&ved=1t:429,r:0,s:0,i:109 • http://www.shmoop.com/points-vectors-functions/bounded-unbounded-functions-exercises.html • http://www.wikipedia.org/ • Youtube.com • Yahoooanswers.com • http://www.google.com/imgres?um=1&hl=en&sa=N&tbo=d&biw=1366&bih=643&tbm=isch&tbnid=You4eUX6EmOMaM:&imgrefurl=http://fromamathclass.blogspot.com/2012/07/idea-function-moves.html&docid=ZO9-8xOM0lLawM&imgurl=http://1.bp.blogspot.com/-N1GYAqOe4Y8/T_MCxZLc3PI/AAAAAAAAAAM/IWT8bAPZBBk/s1600/mathematical-dance-moves.jpg&w=600&h=536&ei=Dmv8UK2AOInY8gSp84HACg&zoom=1&iact=hc&vpx=597&vpy=185&dur=168&hovh=212&hovw=238&tx=168&ty=84&sig=108440193668009717289&page=3&tbnh=135&tbnw=142&start=48&ndsp=27&ved=1t:429,r:71,s:0,i:305