sulpcegu5e ppt 2_1
TRANSCRIPT
![Page 1: Sulpcegu5e ppt 2_1](https://reader036.vdocument.in/reader036/viewer/2022062419/55824094d8b42a0d368b5326/html5/thumbnails/1.jpg)
Section 2.1
Functions
![Page 2: Sulpcegu5e ppt 2_1](https://reader036.vdocument.in/reader036/viewer/2022062419/55824094d8b42a0d368b5326/html5/thumbnails/2.jpg)
OBJECTIVE 1
![Page 3: Sulpcegu5e ppt 2_1](https://reader036.vdocument.in/reader036/viewer/2022062419/55824094d8b42a0d368b5326/html5/thumbnails/3.jpg)
A relation is a correspondence between two sets.
If x and y are two elements in these sets and if a relation exists between x and y, then we say that x corresponds to y or that y depends on x, and we write x y.
![Page 4: Sulpcegu5e ppt 2_1](https://reader036.vdocument.in/reader036/viewer/2022062419/55824094d8b42a0d368b5326/html5/thumbnails/4.jpg)
![Page 5: Sulpcegu5e ppt 2_1](https://reader036.vdocument.in/reader036/viewer/2022062419/55824094d8b42a0d368b5326/html5/thumbnails/5.jpg)
![Page 6: Sulpcegu5e ppt 2_1](https://reader036.vdocument.in/reader036/viewer/2022062419/55824094d8b42a0d368b5326/html5/thumbnails/6.jpg)
FUNCTION
![Page 7: Sulpcegu5e ppt 2_1](https://reader036.vdocument.in/reader036/viewer/2022062419/55824094d8b42a0d368b5326/html5/thumbnails/7.jpg)
![Page 8: Sulpcegu5e ppt 2_1](https://reader036.vdocument.in/reader036/viewer/2022062419/55824094d8b42a0d368b5326/html5/thumbnails/8.jpg)
![Page 9: Sulpcegu5e ppt 2_1](https://reader036.vdocument.in/reader036/viewer/2022062419/55824094d8b42a0d368b5326/html5/thumbnails/9.jpg)
![Page 10: Sulpcegu5e ppt 2_1](https://reader036.vdocument.in/reader036/viewer/2022062419/55824094d8b42a0d368b5326/html5/thumbnails/10.jpg)
Determine whether each relation represents a function. If it is a function, state the domain and range.
{(-2, 3), (4, 1), (3, -2), (2, -1)}
{(2, 3), (4, 3), (3, 3), (2, -1)}
{(2, 3), (4, 1), (3, -2), (2, -1)}
![Page 11: Sulpcegu5e ppt 2_1](https://reader036.vdocument.in/reader036/viewer/2022062419/55824094d8b42a0d368b5326/html5/thumbnails/11.jpg)
Determine if the equation defines y as a function of x.
13
2y x
Determine if the equation defines y as a function of x.
22 1x y
![Page 12: Sulpcegu5e ppt 2_1](https://reader036.vdocument.in/reader036/viewer/2022062419/55824094d8b42a0d368b5326/html5/thumbnails/12.jpg)
OBJECTIVE 2
![Page 13: Sulpcegu5e ppt 2_1](https://reader036.vdocument.in/reader036/viewer/2022062419/55824094d8b42a0d368b5326/html5/thumbnails/13.jpg)
![Page 14: Sulpcegu5e ppt 2_1](https://reader036.vdocument.in/reader036/viewer/2022062419/55824094d8b42a0d368b5326/html5/thumbnails/14.jpg)
FUNCTION MACHINE
![Page 15: Sulpcegu5e ppt 2_1](https://reader036.vdocument.in/reader036/viewer/2022062419/55824094d8b42a0d368b5326/html5/thumbnails/15.jpg)
The name of the function is f.
The independent variable or argument of f is p.
2f p p
q is called the dependent variable If q f p 3 9f
9 is the value of f at 3 or 9 is the image of 3.
State the domain and the range of f.
![Page 16: Sulpcegu5e ppt 2_1](https://reader036.vdocument.in/reader036/viewer/2022062419/55824094d8b42a0d368b5326/html5/thumbnails/16.jpg)
2For the function defined by 3 2 , evaluate:f f x x x
![Page 17: Sulpcegu5e ppt 2_1](https://reader036.vdocument.in/reader036/viewer/2022062419/55824094d8b42a0d368b5326/html5/thumbnails/17.jpg)
![Page 18: Sulpcegu5e ppt 2_1](https://reader036.vdocument.in/reader036/viewer/2022062419/55824094d8b42a0d368b5326/html5/thumbnails/18.jpg)
![Page 19: Sulpcegu5e ppt 2_1](https://reader036.vdocument.in/reader036/viewer/2022062419/55824094d8b42a0d368b5326/html5/thumbnails/19.jpg)
(a) For each x in the domain of f, there is exactly one image f(x) in the range; however, an element in the range can result from more than one x in the domain.
(b) f is the symbol that we use to denote the function. It is symbolic of the equation that we use to get from an x in the domain to f(x) in the range.
(c) If y = f(x), then x is called the independent variable or argument of f, and y is called the dependent variable or the value of f at x.
SummaryImportant Facts About Functions
![Page 20: Sulpcegu5e ppt 2_1](https://reader036.vdocument.in/reader036/viewer/2022062419/55824094d8b42a0d368b5326/html5/thumbnails/20.jpg)
OBJECTIVE 3
![Page 21: Sulpcegu5e ppt 2_1](https://reader036.vdocument.in/reader036/viewer/2022062419/55824094d8b42a0d368b5326/html5/thumbnails/21.jpg)
2
4(a)
2 3
xf x
x x
2(b) 9g x x
(c) 3 2h x x
![Page 22: Sulpcegu5e ppt 2_1](https://reader036.vdocument.in/reader036/viewer/2022062419/55824094d8b42a0d368b5326/html5/thumbnails/22.jpg)
![Page 23: Sulpcegu5e ppt 2_1](https://reader036.vdocument.in/reader036/viewer/2022062419/55824094d8b42a0d368b5326/html5/thumbnails/23.jpg)
A rectangular garden has a perimeter of 100 feet. Express the area A of the garden as a function of the width w. Find the domain.
wA
![Page 24: Sulpcegu5e ppt 2_1](https://reader036.vdocument.in/reader036/viewer/2022062419/55824094d8b42a0d368b5326/html5/thumbnails/24.jpg)
OBJECTIVE 4
![Page 25: Sulpcegu5e ppt 2_1](https://reader036.vdocument.in/reader036/viewer/2022062419/55824094d8b42a0d368b5326/html5/thumbnails/25.jpg)
![Page 26: Sulpcegu5e ppt 2_1](https://reader036.vdocument.in/reader036/viewer/2022062419/55824094d8b42a0d368b5326/html5/thumbnails/26.jpg)
![Page 27: Sulpcegu5e ppt 2_1](https://reader036.vdocument.in/reader036/viewer/2022062419/55824094d8b42a0d368b5326/html5/thumbnails/27.jpg)
2 3For the functions 2 3 4 1
find the following:
f x x g x x
![Page 28: Sulpcegu5e ppt 2_1](https://reader036.vdocument.in/reader036/viewer/2022062419/55824094d8b42a0d368b5326/html5/thumbnails/28.jpg)