1. The document discusses functions and their graphs. 2. It defines a vertical line test to determine if a graph represents a function and provides examples of graphs that both do and do not represent functions. 3. It introduces function notation using f(x) and provides examples of evaluating functions for given values of x.

1. 2-1: Functions & Their Graphs
Objectives:
1. I will determine if a function is linear.
2. I will find the given value of the function.
3. I will graph linear functions.

2. Graphs of a Function
Vertical Line Test:
If a vertical line is passed over
the graph and it intersects the
graph in exactly one point, the
graph represents a function.

3. Does the graph represent a function?
Name the domain and range.
Yes
x D: all reals
R: all reals
y
Yes
x D: all reals
R: y ≥ -6
y

4. Does the graph represent a function?
Name the domain and range.
No
x D: x ≥ 1/2
R: all reals
y
No
x D: all reals
R: all reals
y

5. Does the graph represent a function?
Name the domain and range.
Yes
x D: all reals
R: y ≥ -6
y
No
x D: x = 2
R: all reals
y

6. Function Notation
• When we know that a relation is a
function, the “y” in the equation can
be replaced with f(x).
• f(x) is simply a notation to designate a
function. It is pronounced ‘f’ of ‘x’.
• The ‘f’ names the function, the ‘x’ tells
the variable that is being used.

7. Value of a Function
Since the equation y = x - 2
represents a function, we can also
write it as f(x) = x - 2.
Find f(4):
f(4) = 4 - 2
f(4) = 2

8. Value of a Function
If g(s) = 2s + 3, find g(-2).
g(-2) = 2(-2) + 3
=-4 + 3
= -1
g(-2) = -1

9. Value of a Function
If h(x) = x2 - x + 7, find h(2c).
h(2c) = (2c)2 – (2c) + 7
= 4c2 - 2c + 7

10. Value of a Function
If f(k) = k2 - 3, find f(a - 1)
f(a - 1)=(a - 1)2 - 3
(Remember FOIL?!)
=(a-1)(a-1) - 3
= a2 - a - a + 1 - 3
= a2 - 2a - 2