1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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)

9. 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

10. 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