Functions - Functions 1 What is a RELATION An Association A...

Info icon This preview shows pages 1–15. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Functions
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
What is a RELATION? An Association A Relationship e.g. “X is less than Y” “X is a factor of Y” “X is the mother of Y”
Image of page 2
RELATION vs. FUNCTION Well-behaved Relation
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
4 A function is a rule that assigns to each input member in a set to a unique output member in another set we call these assignments a function which we can denote by f, we say that “f is a function of A into B” which we write as f: A B Functions
Image of page 4
5 Functions Def n : Suppose A is a non-empty set. if is an input element then the element in B which is assigned to a is denoted by f(a). Then we have a function. Let’s denote this function by f. A is said to be the domain of f. The domain of f is denoted by D(f). (collection of all the possible input members) A a
Image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
6 not a function function A f e.g., D(f) = {1, 4, 7, 9}, f(1)=10, f(4)=0, f(7)=3, f(9)=6 not a function f f A A
Image of page 6
7 Set which consists of all the members in B is call co-domain and set which consists of all outputs members is called the range(E) A B Domain Range Co-domain
Image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
8 Function as a mapping from one set to another set If A and B are two sets then a function f of A into B is called a mapping of A into B. We say that f maps A into B and we write this as f: A B
Image of page 8
9 if the domain and co-domain of a function f are the same set, then f: A A Then f is called a “transformation” on A
Image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
10 Variables A variable that represent input numbers for a function is called an “independent variables” . A variable that represent output numbers for a function is called a “dependent variables” .
Image of page 10
11 we say that the dependent variable is a function of the independent variable. Consider the bellow equation Y=2x+5 In this, x is the independent variable and y is the is the dependent variable. y is a function of x.
Image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
12 Let A={1,2,3,4} B={1,2,3,4,5,6,7} Consider f: A B Where f(x)=x+2 The domain of the function is A and the co- domain is B. Range of f is f(1)=1+2=3 f(2)=2+2=4 f(3)=3+2=5 f(4)=4+2=6 that is Range E={3,4,5,6}
Image of page 12
13 1 2 3 4 3 4 5 6 1 2 7 Domain Co-domain Range A B f
Image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
14 Consider y 2 =x In this case y is not a function in x because when the input value of x is 9, y 2 =9 gives two output values y= +3 or -3. this goes same for x=4,16,25,…..
Image of page 14
Image of page 15
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern