Advanced Algebra Notes Section 2.1: Represent Relations & Functions relation A is a mapping, or pairing, of input and output values. (A set of ordered pairs) The 1st number in an ordered pair (Input value) is called the or . The 2nd number in an ordered pair (Output value) is called the x-coordinate domain y-coordinate range

relation A shows how each member of the domain is paired with each member of the range. A is a special relation in which each element of the domain is paired with exactly one element of the range. This is what is called one-to-one correspondence. function

Example 1: Identify the domain and range of the relation and tell whether the relation is a function. Input Output Domain = { -3, -1, 2, 4 } Range = { -4, 2, 3 } -3 -1 2 4 2 3 -4 YES

Example 2: Represent the relation as a graph and a mapping diagram Example 2: Represent the relation as a graph and a mapping diagram. {(-5,4), (-1,0), (3,-1), (3,5)} Is the relation a function? -5 -1 3 4 -1 5 NO

When you are trying to determine if the graph of a relation is a function you will use the . If the vertical line intersects the graph in two or more places then the relation is not a function, but if it only intersects in one place then it is a function. vertical line test

solution equation in two variables independent variable Many functions can be described by an , such as y= -2x+5. The input variable(x) is called the The output variable(y) is called the because it depends on the value of the input variable. An ordered pair (x, y) is a of an equation in 2 variables if substituting x and y in the equation produces a true statement. Ex: y=3x–5, (2, 1) is a solution because 1=3(2)-5 is true. equation in two variables independent variable dependent variable solution

graph linear function linear function The of an equation in 2 variables is the set of all points (x, y) that represents solutions of the equation. The graph of an equation in 2 variables is a if the equation is of the form y = mx + b. The equation y = 3x – 5 is an example of a . You can write a linear function in function notation by replacing the variable y with f(x) to get f(x) = mx+b. We read f(x) as “the value of x” or simply “f of x” linear function linear function

y= -2(0)+1=1 (0,1) (0,-4) (1,-1) y= -2(1)+1=-1 (3,-2) Graph the equation/functions: y=-2x+1 f(x)=2/3 x-4 y= -2(0)+1=1 (0,1) f(x)=2/3(0)-4 =-4 (0,-4) (1,-1) y= -2(1)+1=-1 f(x)=2/3(3)-4=-2 (3,-2)

We will also classify a function as linear or not then evaluate the function. A function is linear if its graph is a or if the equation has the x variable raised to the power and the x-variable is not in the or inside an line first denominator exponent

NO YES f(x) = 2(-3*-3*-3)+5 f(x) = 12 – 8(-3) f(x) = 2(-27)+5 Tell whether the function is linear and then evaluate when x = -3 NO YES f(x) = 2(-3*-3*-3)+5 f(x) = 12 – 8(-3) f(x) = 2(-27)+5 f(x) = 12 – (-24) f(x) = -54+5 f(x) = 36 f(x) = -49