Date post: | 29-Jan-2016 |
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Graphs of Functions
The graph of a function gives you a visual representation
of its rule. A set of points generated like we did in the previous
section.
You can determine if a given graph is a true function by the
VERTICAL LINE TEST. Given the graph of a relation, the
vertical line test is used to check if that relation is a function.
The vertical line CAN NOT touch the graph in more than 1 spot.
Graphs of Functions
VERTICAL LINE TEST – a vertical line drawn anywhere on the graph
CAN NOT intersect the graph more than once.
Here is the graph of a relation.
Is it a true function ?
Graphs of Functions
VERTICAL LINE TEST – a vertical line drawn anywhere on the graph
CAN NOT intersect the graph more than once.
Here is the graph of a relation.
Is it a true function ?
YES…I can not draw a vertical line that passes thru the graph more than once
Graphs of Functions
VERTICAL LINE TEST – a vertical line drawn anywhere on the graph
CAN NOT intersect the graph more than once.
Here is the graph of a relation.
Is it a true function ?
Graphs of Functions
VERTICAL LINE TEST – a vertical line drawn anywhere on the graph
CAN NOT intersect the graph more than once.
Here is the graph of a relation.
Is it a true function ?
NO…I only need to find one spot where a vertical line crosses more than one time.
Graphs of Functions
One-to-One Functions – a function where each range value has one and ONLY one domain value.
Horizontal line test checks for one-to-one…
Here is the graph of a function.
Is it one-to-one ?
Graphs of Functions
One-to-One Functions – a function where each range value has one and ONLY one domain value.
Horizontal line test checks for one-to-one…
Here is the graph of a function.
Is it one-to-one ?
NO…I only need to find one spot where a horizontal line crosses more than one time.
Graphs of Functions
One-to-One Functions – a function where each range value has one and ONLY one domain value.
Horizontal line test checks for one-to-one…
Here is the graph of a function.
Is it one-to-one ?
Graphs of Functions
One-to-One Functions – a function where each range value has one and ONLY one domain value.
Horizontal line test checks for one-to-one…
Here is the graph of a function.
Is it one-to-one ?
YES…I can not draw a vertical line that crosses more than one time.
Graphs of Functions
One-to-One Functions – a function where each range value has one and ONLY one domain value.
Horizontal line test checks for one-to-one…
Functions that are not one-to-one have NO INVERSE !!!
Graphs of Functions
Graphing functions falls into two categories…
1. Continuous or constant functions ( no breaks )
2. Piecewise functions…breaks in the graph occur
We will first look at the Continuous Functions…
Steps : 1. Create a table of values for f(x)
2. Plot the points and sketch your graph
Graphs of Functions
Steps : 1. Create a table of values for ƒ(x)2. Plot the points and sketch your graph
EXAMPLE : Graph ƒ(x) = x2 – 5
Graphs of Functions
Steps : 1. Create a table of values for ƒ(x)2. Plot the points and sketch your graph
EXAMPLE : Graph ƒ(x) = x2 – 5
x f(x)
- 2 -1
f(-2) = (-2)2-5
f(-2) = 4 – 5
f(-2) = -1
Graphs of Functions
Steps : 1. Create a table of values for ƒ(x)2. Plot the points and sketch your graph
EXAMPLE : Graph ƒ(x) = x2 – 5
x f(x)
- 2 -1
- 1 - 4
f(-1) = (-1)2-5
f(-1) = 1 – 5
f(-1) = - 4
Graphs of Functions
Steps : 1. Create a table of values for ƒ(x)2. Plot the points and sketch your graph
EXAMPLE : Graph ƒ(x) = x2 – 5
x f(x)
- 2 -1
- 1 - 4
0 - 5
f(0) = (0)2-5
f(0) = 0 – 5
f(0) = - 5
Graphs of Functions
Steps : 1. Create a table of values for ƒ(x)2. Plot the points and sketch your graph
EXAMPLE : Graph ƒ(x) = x2 – 5
x f(x)
- 2 -1
- 1 - 4
0 - 5
1 - 4
f(1) = (1)2-5
f(1) = 1 – 5
f(1) = - 4
Graphs of Functions
Steps : 1. Create a table of values for ƒ(x)2. Plot the points and sketch your graph
EXAMPLE : Graph ƒ(x) = x2 – 5
x f(x)
- 2 -1
- 1 - 4
0 - 5
1 - 4
2 - 1
f(2) = (2)2-5
f(2) = 4 – 5
f(2) = -1
Graphs of Functions
Steps : 1. Create a table of values for ƒ(x)2. Plot the points and sketch your graph
EXAMPLE : Graph ƒ(x) = x2 – 5
x f(x)
- 2 -1
- 1 - 4
0 - 5
1 - 4
2 - 1
Plot the points…
Graphs of Functions
Steps : 1. Create a table of values for ƒ(x)2. Plot the points and sketch your graph
EXAMPLE : Graph ƒ(x) = x2 – 5
x f(x)
- 2 -1
- 1 - 4
0 - 5
1 - 4
2 - 1
Sketch your graph…
Graphs of Functions
Steps : 1. Create a table of values for ƒ(x)2. Plot the points and sketch your graph
EXAMPLE : Graph ƒ(x) = x3 + 2
x f (x)
-3 - 25
f(-3) = (-3)3 + 2
f(-3) = - 27 + 2
f(-3) = -25
Graphs of Functions
Steps : 1. Create a table of values for ƒ(x)2. Plot the points and sketch your graph
EXAMPLE : Graph ƒ(x) = x3 + 2
x f (x)
-3 - 25
-2 -6
f(-2) = (-2)3 + 2
f(-2) = -8 + 2
f(-2) = -6
Graphs of Functions
Steps : 1. Create a table of values for ƒ(x)2. Plot the points and sketch your graph
EXAMPLE : Graph ƒ(x) = x3 + 2
x f (x)
-3 - 25
-2 -6
-1 1
f(-1) = (-1)3 + 2
f(-1) = -1+ 2
f(-1) = 1
Graphs of Functions
Steps : 1. Create a table of values for ƒ(x)2. Plot the points and sketch your graph
EXAMPLE : Graph ƒ(x) = x3 + 2
x f (x)
-3 - 25
-2 -6
-1 1
0 2
f(0) = (0)3 + 2
f(0) = 0+ 2
f(0) = 2
Graphs of Functions
Steps : 1. Create a table of values for ƒ(x)2. Plot the points and sketch your graph
EXAMPLE : Graph ƒ(x) = x3 + 2
x f (x)
-3 - 25
-2 -6
-1 1
0 2
1 3
f(1) = (1)3 + 2
f(1) = 1 + 2
f(1) = 3
Graphs of Functions
Steps : 1. Create a table of values for ƒ(x)2. Plot the points and sketch your graph
EXAMPLE : Graph ƒ(x) = x3 + 2
x f (x)
-3 - 25
-2 -6
-1 1
0 2
1 3
2 10
f(2) = (2)3 + 2
f(2) = 8 + 2
f(2) = 10
Graphs of Functions
Steps : 1. Create a table of values for ƒ(x)2. Plot the points and sketch your graph
EXAMPLE : Graph ƒ(x) = x3 + 2
x f (x)
-3 - 25
-2 -6
-1 1
0 2
1 3
2 10
3 29
f(3) = (3)3 + 2
f(3) = 27 + 2
f(3) = 29
Graphs of Functions
Steps : 1. Create a table of values for ƒ(x)2. Plot the points and sketch your graph
EXAMPLE : Graph ƒ(x) = x3 + 2
x f (x)
-3 - 25
-2 -6
-1 1
0 2
1 3
2 10
3 29
Plot your points…
Graphs of Functions
Steps : 1. Create a table of values for ƒ(x)2. Plot the points and sketch your graph
EXAMPLE : Graph ƒ(x) = x3 + 2
x f (x)
-3 - 25
-2 -6
-1 1
0 2
1 3
2 10
3 29
Sketch the graph…