1. Functions Relation Vertical Line Test Domain
1.2 Functions & Graphs
Functions
Relation
Vertical Line Test
Domain

2. Functions
A function is a correspondence between a first set, called the domain, and a second set, call the range, such that each member of the domain corresponds to exactly one member of the range.
Relation
A relation is a correspondence between a first set, called the domain, and a second set, call the range, such that each member of the domain corresponds to at least one member of the range.

3. Does the following describe y as a function of x?
The table below shows record low temperatures, in degrees Fahrenheit, in Orlando, FL
Date in October, x 19 20 21 22 23 24
lowest temperature, y 52 65 69 72 67 58
The relationship between a student’s IQ x, and their SAT score, y.
A person’s weight x, as a function of their height y.
x (lbs)
125
200
110
107
132
y (in) 64 72 60
59.00 68 66

4. Does the table represent a function? Find the domain and range.
Functions
Let y = f(x)
Does the table represent a function?
Find the domain and range.
What is the input when the output is -6?
Find f(4)
Find x such that f(x)=9. x 4 7 24 50
f(x) 9 12 -6 58
-19

5. Given f (x) = -3x+4, evaluate
f (5a)
f (a+1)
Given 𝑓 (𝑥) = 2 − 𝑥 2 , evaluate
f (a+2)

6. The graph of a function f is the set of all points on the plane of the form (x, f(x)). Vertical Line Test If it is possible for a vertical line to cross a graph more than once, then the graph is not the graph of a function.

7. Is this a function? Why?
Is this a linear Function? Why?
Find f(1).
Find f(x) when x = 2.
Find the inputs when the output is -2.
Find the values of x for which f(x)=0.
Domain?
Range?

8. Domain - the set of all possible values of x (input)
Domain - the set of all possible values of x (input). (Independent Variable)
Range – the set of all possible values of y (output) (Dependent Variable)
Domain Restrictions:
Exclude any x-values that result in division by zero.
Exclude any x-values that result in even roots of negative numbers
Find Domain a. f(x) = 2x b.
c d. 𝑓(𝑥) = 1 𝑥+3

9. Is this a function? Why?
Is this a linear Function? Why?
x-intercepts?
y-intercepts?
Find f(-1)
Find f(x) when x = -2.
Find the inputs when the output is -5.
Find the values of x for which f(x)=0.
Domain?
Range?