Download 2-1 Represent relations and functions

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What is a relation?
Represent relations and
functions
• A relation is when an input is paired with an
output.
• Relations can be in the form of ordered pairs,
tables, graphs, or mapping diagrams.
2.1
What is input/output?
• The input refers to the x value or domain of
relation.
• The output refers to the y value or range of
the relation.
Identify the domain and range
• (-2, -3), (-1, -1), (1, 3), (2, 2), and (3, 1)
• Domain: {-2, -1, 1, 2, 3}
• Range: {-3, -1, 3, 2, 1} {-3, -1, 1, 2, 3}
• Make a Mapping Diagram
-2
-1
1
2
3
-3
-1
1
2
3
1
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Is it a function?
What is a function?
• A function is a specific kind of relation,
therefore all functions are relations.
• Functions have exactly one input mapped to
an output value.
• In other words each x-value has to be unique,
no repeating x-values.
X-values cannot repeat,
•
•
•
•
(4, 5), (5, 6), (6, 7), (7, 7)
Yes, each x-value is different
(-2, 0), (4, 8), (9, -1), (-2, 0)
Yes, (-2, 0) is the same point and was
accidentally listed twice.
• (-3, 9), (-2, 1), (7, 9), (3, 0), (-2, 10)
• No, the -2 is paired with more than 1 y-value.
X-values cannot repeat,…
Is it a function?
• Yes, each x-value only
has 1 arrow coming
from it.
• No, the 1 has two
arrows coming from it,
so the 1 is mapped to
two y-values and the 1
repeats
• Domain: {-4, -2, 0, 1, -2} {-4, -2, 0, 1} Not a
function
• Range:x{3, 1,y 3, -2, -4} {-4, -2, 1, 3}
-4 3
-2 -4
-4
-4
-2
-2
-2 1
1
0
0
3
3
1
1 -2
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What is the vertical line test?
• Yes, each x-value is unique.
What are linear equations
Linear equations can be written in the form
mx+b.
• This graph does
not pass the
vertical line test
when x = 28.
• This graph does pass the
vertical line test so it is a
function.
They cannot look like:
They can look like:
• y = x2+1, no x2 or y2
• y = 2x + 1
• y = |2x+1|, no absolute
values
• 2x + 3y = 5
•
= 2 + 1, no square
roots
•
= , x can’t be in the
denominator
y=
• ½x+7=y
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Graphing Linear equations
• Before you start to graph any linear equation, you
should solve the equation for y so that it is in
y = mx + b form.
Examples
• Graph:
• y = -2x + 1
• Graph:
• 2y – 3x = -8
• The b is the y-intercept so you plot the first point
on the y-axis on whatever numeric value the b is.
• The m is the slope, so from the b-value you count
the rise and then run to make the line.
Function notation
Normal linear equation
Function Notation
• y = mx + b
• f(x) = mx + b
• Function notation is just a fancy way of
representing the y for all functions.
• Solve: y = 3x + 1, when x = 2 • Solve: f(2) = 3x + 1
• So in function notation y is the same thing as
f(x)
• Solve: y = ½x – 3, when x = 8
• Solve: f(8) = ½x – 3
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Determine whether it is a linear
function, then solve
• f(3) = 2x2 –x +1
• f(5) = 7 – 3x
•
•
•
•
P(33) = 1 + 0.03d
P(33) = 1 + 0.03(33)
P(33) = 1+0.99
P(33) = 1.99
• Domain: 0 < d < 35,800
• Range: We need to find P(35,800) to determine
the highest y-value
• P(35,800) = 1+0.03(35,800)
• P(35,800) = 1 + 1074
• P(35,800) =1075
• Range: 1< P(d) < 1075
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