Sat math Essentials

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9 0

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f
(
x
) 
8
x
2
becomes 
f
(3) 
8(3) 
2
f
(3) 
24 
2 
22
So, when 
x
3, the value of the function is 22.
Potential functions must pass the 
vertical line test
in order to be considered a function. The vertical line test
is the following: Does any vertical line drawn through a graph of the potential function pass through only one point
of the graph? If YES, then any vertical line drawn passes through only one point, and the potential function is a
function. If NO, then a vertical line can be drawn that passes through more than one point, and the potential func-
tion is 
not
a function.
The graph below shows a function because any vertical line drawn on the graph (such as the dotted verti-
cal line shown) passes through the graph of the function only once:
The graph below does NOT show a function because the dotted vertical line passes five times through the
graph:
x
y
x
y
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A L G E B R A R E V I E W
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9 1

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All of the 
x
values of a function, collectively, are called its 
domain
. Sometimes there are 
x
values that are out-
side of the domain, but these are the 
x
values for which the function is not defined.
All of the values taken on by 
f
(
x
) are collectively called the 
range
. Any values that 
f
(
x
) cannot be equal to are
said to be outside of the range.
The 
x
values are known as the