2-1 Relations and Functions
Analyze and Graph relations
Domain and Range
In a Function the input is Domain,
normally x is used for the input
The output is the Range,
normally y is used for the output
Other names
Domain is the set of possible inputs, thus it is
the Independent Variable (meaning this is
the one you get to pick to use) in the function.
Range is the set of possible outcomes, thus it is
the Dependent Variable ( meaning it is value
dependents on the input) in the function.
Every element in the Domain go to one
element in the Range
a
b
c
1
2
3
This is a function, since element in the domain maps
to one element in the range.
Even if b and c both map to 2
Every element in the Domain go to one
element in the Range
a
b
c
1
2
3
This is NOT a function, since b in the domain maps
to 2 and 3 in the range.
Vertical Line Test
If you pass a vertical line through a graph of a
relation and it touches the graph in two or
more points, then the graphed relation is not
a function.
Lets talk about graphing
We have to thank Rene Descartes for graphing.
René Descartes French: ; (31 March 1596 – 11 February 1650)
Descartes' influence in mathematics is equally apparent; the Cartesian
coordinate system—allowing algebraic equations to be expressed as
geometric shapes (2D coordinate system)—was named after him. He is
credited as the father of analytical geometry, the bridge between algebra and
geometry, crucial to the discovery of infinitesimal calculus and analysis.
The Cartesian coordinate plane
Broken into 4 Quadrants
II (two)
III (three)
How to remember the Quadrants?
I (one)
IV (four)
Which one is the X axis or Y axis?
The x axis is horizontal
The y axis is vertical
This gives order pairs
(x, y) as points
Which one is the X axis or Y axis?
The x axis is horizontal
The y axis is vertical
This gives order pairs
(x, y) as points
(8, 3)
8 over and 3 up
Graphing a function
Set up an input/output table where x is the input
and the output is the y. Give the equation y =
2x + 1. Place the points on the plane and
connect the dots.
(x y)
(2,5)
(1 3)
(1, 3)
(2 5)
(-1, -1)
(-1 - 1)
Lets graph x =
2
y
+1
Here we will put in y and solve for x
(x, y)
(1, 0)
x = 02 + 1
(2, 1)
x = 12 + 1
(2, -1) x = (- 1)2 + 1
1
(10, 3) x = (3)2 + 1
( 10, - 3) x = (- 3)2 + 1
Is x =
2
y
+ 1 a function?
Is x =
2
y
+ 1 a function?
No, it does not pass the Vertical line test.
What is its domain?
Is x =
2
y
+ 1 a function?
No, it does not pass the Vertical line test.
What is its domain?
x≥1
How would you solve f(2) = 4x + 1
Replace x with 2
f(2) = 4(2) + 1
f(2) = 9
Homework
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