Hannah Kiiskilaand

Mitch Pronga

12 Basic Functions

http://www.youtube.com/watch?v=M87p94A1dL8

Introduction Video

Intro

The 12 Basic Functions

Find the Domain

https://www.youtube.com/watch?v=2tC36VPxCmw

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

Finding the Domain of a Function Ex.

Y X

-100 -100

0 0

100 100

Y=[X] is the equation of this graphThis is table for the second basic

function.

The domain would be (- , )

Ex. 2

y x

-100 -100

0 0

100 100

This is because all the values of Y Will give out a real X value

https://www.youtube.com/watch?v=4kCHuVrtbc4

Find the Range

This is the graph of the function Y=x^2To find the range you need to lookat the graph to see what values of ythe 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.

Finding the Range of a Function Ex.

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

graph reaches all values of y.

Ex. 2

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.

Bounded Above

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.

Bounded Below

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.

Bounded

http://quizlet.com/415738/scatter/ Go to the 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!

Quizlet Activity

A. Squaring FunctionB. Reciprocal FunctionC. Square Root FunctionD. Greatest Integer Function

1. What is this graphs name?

A. Sine FunctionB. Cubing FunctionC. Exponential Growth FunctionD. Basic Logistic Function

2. What is this graphs name?

A. Reciprocal FunctionB. Sine FunctionC. Natural Logarithmic FunctionD. Greatest Integer Function

3. What is the name of this graph?

A. Greatest Integer FunctionB. Cosine FunctionC. Identity FunctionD. Basic Logistic Function

4. What is this graphs name?

A. Cubing FunctionB. Reciprocal FunctionC. Exponential Growth FunctionD. Cosine Function

5. What is this graphs name?

A. AboveB. BelowC. BothD. Neither

6. How is this graph bounded?

A. Above B. BelowC. BothD. Neither

7. How is this graph bounded?

A. (-1, 1)B. (- , )C. [-1,1]D. [- , ]

8. What is the range of this graph?

A. (- , ) B. (0, ) C. [- , ]D. [- 0, )

9. What is the domain of this graph?

A. Identity Function, (- , ), (- , )

B. Identity Function, (- , 0] [1, ), (- , )

C. Identity Function, [- , ], [- , ]

D. Squaring Function, [- , ], [- , ]

10. What is the name, range, and domain of this graph?

1. C2. D3. B4. A5. B6. B7. C8. C9. A10. A

Answer Key

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

Bibliography