Algebra 2 (2-1 relations and functions)

Domain

The set of all X - coordinates in a relation; input

Relation

A pairing of input values with output values; a set of ordered pairs; can be represented numerically (-3,4) or graphically (coordinate place or mapping).

Linear equation

A representation of a function in 2 variables Ex: y=3x +4

Step function

A type of piecewise function whose graph resembles a set of stair steps

A function is:

—Linear if it can be written in the form f(x)=mx+b —Not linear if any exponents on the X or Y Ex: f(x)=x2+1 Evaluate when x=-1 —evaluate f(2) by looking at the graph— look at 2 on the x axis, find its y ordered pair partner

Writing piecewise functions

1. Figure out the equation for each line—. y=mx+b 2. Figure out constraints (domain)

Steps to graphing a piecewise function

1. Graph first function IP pencil (will erase later) 2. Look at the functions in equality. since X >3 put an OPEN circle on where the graph lines up with the three on the X axis. Earse everything NOT greater than 3. 3. Graph the second function 4. Look at the functions inequality. Since X <_ 3, put a close circle on where the graph lines up with the 3 on the X axis. Erase everything NOT less than or equal to 3. 5. Repeat for other functions if any.

Piecewise functions

A function represented by a combination of equations - they have different rules for different parts of it don't mean POD: Given h(x)=3/2 x + 5/2, evaluate h(-5) h (-5)= 3/2 (-5) +5/2 h(-5) -15/2 + 5/2 = -10/2= -5

vertical line test

A relation is NOT a function if a vertical line can be drawn on a graph so that the line touches the graphs in more than one spot.

Function

A type of relation in which each member of the domain has exactly one partner in the range; x- values (input) cannot repeat

Determine whether the function is linear

Evaluate F(3) ....(when x=3, what is y?) Linear vs Nonlinear ——-see notes

An ordered pair (x,y) is a solution if the equation is true when those values are plugged in

Ex: (1,7) is a solution to y= 3x+4 since 7=3(1) +4 7=7

Brackets

Including [ , ] same as _<, _>

Represent everything with inequalities or ______________

Interval notation

Function notation

Replace is y with f(x) f(x)=3x+4 means y=3x+4

Evaluating a piecewise function

The inequalities tell you which equation to plug the X value into F(x)= 3x+2 If x <_ 3 X-1 if x>3

Range

The set of all y- coordinates in a relation; output

Parentheses

Up to but not including ( , ), same as < & >