Download 1.3 Functions and Their Representation | MATH 1111 - College Algebra and more Quizzes Algebra in PDF only on Docsity!
Function
A relation between two sets of numbers with a restriction were each element of the domaincorrespondsto only one element in the rangeexample: f(x): x TERM 2
f(x)
DEFINITION 2 -effofex f is a function of x.example: The amount of money I spend on food I buy depends on the number of people in my household at the time. Money= f (#of people)f(x)= $100(x) TERM 3
Inputs
DEFINITION 3
- what goes into a function to get an outcome example: if your paycheck is a function of hours worked 40 hours X wage = paycheck amount40 hours is your Input and also your domain TERM 4
Outputs
DEFINITION 4
- the outcome of a functionexample: if your paycheck is a function of hours worked 40 hours X wage = paycheck amount40 hours is your Input and also your domain TERM 5
Relations
DEFINITION 5
- a set of ordered pairs for every input there is only one output. example: First names Last names Joe Robinson Bill Smith Jack Rogers Jane Smith Joe JohnsonIn a function, there can be many Joes in class but only one Joe Robinson. It is impossible to have A Bill Smith and a Jane Smith,becausethere should be only one output
Representing Functions
-There are several way to represent functions VerbalRepresentation example: I make $3.35 an hour if I work X number hours 2. NumericalRepresentation example: x(seconds) |1 2 3 4 5 6 7 | y(miles) |0.2 0.4 0.6 0.8 1.0 1.2 1.4| 3. Symbolic Representation (the formula) example: f(x)= x/5, where y= f(x) 4. Graphical Representation (the graph) example: plot:(1,0.2), (2,0.4), (3,0.6), (4, 0.8), (5,1.0) [where X Y] TERM 7
Interval
Notation
DEFINITION 7
- when writing a function interval notation uses just thecoordinatesexample: the domain of a function would be represented as (-4,4] , and the range [-1, 3] TERM 8
Set Builder Notation (preferred by
teacher)
DEFINITION 8
- when writing a function set builder notation uses symbols. (for this card: (<or=to) , (>or=to))example: the domain of afunctionwould be represented as-4<(or=to) x <(or=to) 4, and the range {-1 <(or=to) y <(or=to) 3} TERM 9
Domain Issues
DEFINITION 9 -There are two domain issues1.divisionby zero2. (square roots)if the function does not have a fraction or a square root the answer is all real numbers ( R ) TERM 10
All Real Numbers
DEFINITION 10 -the lines have nodefinedend. (for this card 00 represents infinity)-Domain: All Real numbers( R ) (-00, 00) interval and/or {-00 < x < 00} set builder-Range: y >(or=to) -2 [-2, 00) interval and/or {-2<(or=to) y < 00} set builder
