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Relations, Equations and Functions
Relations
A relation is a set of
ordered pairs, and can be represented by a table, a graph or
a mapping.
A table
A graph
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Mapping
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The solutions of an
equation in two variables is an ordered pair that
results in a true statement when substituted into the
equation.
Linear Equations
A linear equation is the
equation of a straight line, and can be written in the
standard form as: Ax + By = C
Another form of a linear equation is:
y = mx + b, where m is the
slope of the line on the graph, and b is the
point on the y-axis ( y-intercept) where the
line crosses the y-axis on the graph of the equation.
Functions
A function is a relation in
which each element of the domain ( x-axis values) is paired
with exactly one element of the range (y-axis
values).
equation
y = 4x + 7
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function
f(x)
= 4x + 7
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Function
Only one
value of y for all values of x |
Not a
function
More than
one value of y for some values of x |
To find the
value of a function substitute the domain value for
x.
Example:
for the function f(x)
= 2x - 4, find the value of x + 3.
Substitute (x + 3)
for x:
f(x + 3) = 2(x + 3)
- 4 = 2x + 2
Difficult
Example:
If f(x) = 6x - 3,
find the value of 3[ f(x2) - 4 ]
Solve this in 3
steps:
1. find the value of
f(x2).
2. Subtract 4 from
this value.
3. Multiply the
result from step 2 by 3.
Step 1: f(x2)
= 6x2 - 4
Step 2: 6x2
- 4 - 4 = 6x2 - 8
Step 3: 3(6x2
- 8) = 18x2 - 24
© The e-Learning Research Foundation 2007
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