Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.
Upcoming SlideShare
×

# Functions 1

438 views

Published on

• Full Name
Comment goes here.

Are you sure you want to Yes No
Your message goes here
• Be the first to comment

• Be the first to like this

### Functions 1

1. 1. 1Ago 27­06:48 p.m.Interval notationStarter:
2. 2. 2Ago 27­06:48 p.m.
3. 3. 3Ago 27­06:48 p.m.By the end of the lesson you will be able to:• Distinguish between relations and functions.• Recognise the domain and range of a function     from its graph or/and its formula.• Use  GDC to draw graphs of functions.• Manipulate function notation.
4. 4. 4Ago 27­06:48 p.m.RelationsA relation is any set of points on the cartesian plane.A relation is often expressed as an equationconnecting two variables  .
5. 5. 5Ago 27­06:48 p.m.The length side of a square is x. Write the area of the square, A, in terms of x.A group of friends rents a car for their holidays. They have to pay a fixed cost of 350\$ plus \$120 per day. Let C be the cost of renting the car and d the number of days the car is rented. Write C in terms of d.The value of a car depreciates in such a way that when it is t years old,  its value V is given by V=12000e­0.6t. (a) Find the value of the car after 4 years.(b) How long does it take for the car to be worth 6000?A(x) = x2C(d) = 350+120d
6. 6. 6Ago 27­06:48 p.m.A(x) = x2C(d) = 350+120d V(t) =12000e­0.6tA function is a relation in which to each value of xcorresponds one and only one value of y.FunctionsA(x) = x2 independent variable? dependent variable?C(d) = 350+120dindependent variable?independent variable?V(t) =12000e­0.6t dependent variable? dependent variable?
7. 7. 7Ago 27­06:48 p.m.A(x) = x2V(t) =12000e­0.6tFunction notationFind  A(3)Find  x  if A(x) = 100What is the meaning of V(4) ?What is the image  of t=4 ?
8. 8. 8Ago 27­06:48 p.m.Functions can also be given by graphsnot a functionnot a functionWhich of these graphs represent functions? function function functionvertical line test.exe
9. 9. 9Ago 27­06:48 p.m. functio function function for all real numbers but zero functionhttp://www.univie.ac.at/future.media/moe/tests/fun1/grongr.html
10. 10. 10Ago 27­06:48 p.m.The domain of a function is the set of permissiblevalues that x may have.A(x) = x2Domain=Use your GDC to plot the graph of A.Range =The range of a function is the set ofall the images( y ).
11. 11. 11Ago 27­06:48 p.m.The domain of a function is the set of permissiblevalues that x may have.The range of a function is the set of all the images( y ).domainrange
12. 12. 12Ago 27­06:48 p.m.State the domain and range of the function :
13. 13. 13Ago 27­06:48 p.m.State the domain and range of the function :
14. 14. 14Ago 27­06:48 p.m.State the domain and range of the function :
15. 15. 15Ago 27­06:48 p.m.State the domain and range of the function :
16. 16. 16Ago 27­06:48 p.m.State the domain and range of the function :
17. 17. 17Ago 27­06:48 p.m.y = x2 ­ 3x + 5y = 3x + 5 y = x5 ­ 3x3    Polynomial functions.The domain of any polynomial function is the set of realnumbers:
18. 18. 18Ago 27­06:48 p.m.State the domain of the function :Draw the graph of this function with your GDC.Is there any value of x for which you cant calculate thevalue of y ?Domain:
19. 19. 19Ago 27­06:48 p.m.What is the range of this function?
20. 20. 20Ago 27­06:48 p.m.State the domain of the function:Draw the graph of this function with your GDC.Domain:Is there any value of x for which you cant calculate thevalue of y ?
21. 21. 21Ago 27­06:48 p.m.This function is called the reciprocal function. Its graph is a hyperbola.What is the range of this function?
22. 22. 22Ago 27­06:48 p.m.Find the domain and range of:Domain:Draw the graph of this function with your GDC.Is there any value of x for which you cant calculate thevalue of y ?
23. 23. 23Ago 27­06:48 p.m.What is the range of this function?
24. 24. 24Ago 27­06:48 p.m.C  Which graph is not a function?yxxyxyxyD  xy
25. 25. 25Ago 27­06:48 p.m.A  B  C  D  Which graph is  a function? A  B  C  D
26. 26. Attachmentsvertical line test.exe