Download The Graph of a Function

WARM-UP:
Interval Notation is a short way to describe all real numbers between two values.
Think about all of the real numbers between -3 and 4.
Graph 1
Graph 2
-6 -4 -2
0 2
4
6
-6 -4 -2
0
Set-builder Notation:
Interval Notation:
-3 < x < 4
(-3, 4)
2
4
6
Now, think about all of the real numbers between -6 and 2, including -6 and 2.
Graph 1
Graph 2
-6 -4 -2
0 2
4
6
-6 -4 -2
0 2
4
Set-builder Notation:
Interval Notation:
-6 < x < 2
[-6, 2]
6
Use interval notation to describe each statement.
_________________
_________________
_________________
_________________
_________________
_________________
_________________
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1. all of the real numbers between 5 and 12
2. all of the real numbers between -3 and 11, including -3 and 11
3. all of the real numbers between 50 and infinity
4. all of the real numbers between 17 and infinity, including 17
5. all positive real numbers
6. all real numbers between negative infinity and 2
7. all real numbers between negative infinity and 12 including 12
8. all negative real numbers
Section 2.2
The Graph of a Function
Date____________
Theorem: Vertical-line Test – A set of points in the x-plane is the graph of a function if
and only if every vertical line intersects the graph in at most one point.
What does the phrase “if and only if” mean in math?
Draw a few examples of …
Functions
Relations (i.e. not functions)
Obtaining Information from the Graph of a Function: Example 1
a) What are the values of f(0),…
b) What is the domain of f?
1
c) What is the range of f?
-2 π
-π
0
π
2π
d) What are the intercepts of the graph?
-1
e) How often does the line y = 2 intersect
the graph?
f) For what values of x does f(x) = -1?
g) For what values of x is f(x) > 0?
Obtaining Information about the Graph of a Function:
x 1
.
x4
a) Is the point (-6, 1/3) on the graph of f?
Ex 2 Consider the function f ( x) 
b) If x = 9, what f(x)? What is the resulting
point on the graph?
c) If f(x) = -4, what is x? What is the
resulting point on the graph?
d) What is the domain of f?
e) What are the x-intercepts of f?
f) What are the y-intercepts of f?
Interpreting Graphs:
Pay attention to the units of the axes to sort out what’s happening in the graph!
Ex 3 Match the graph with the appropriate description.
A. The height of a football during an incomplete pass as a function of time
B. The unlimited growth of a pair of breeding rabbits as a function of time
C. The height of a pine tree as a function of time
D. The demand for ice cream as a function of temperature
E. The distance a baseball is from home plate as the pitcher and catcher throw the ball
back and forth as a function of time
1.
2.
y
x
3.
y
x
4.
y
x
5.
y
x
y
x