Transcript Boardworks Functions W8

A12 Functions
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Introducing functions
A function is a rule which maps one number,
sometimes called the input or x, onto another
number, sometimes called the output or y.
A function can be illustrated using a function diagram to
show the operations performed on the input.
x
×3
+2
y
A function can be written as an equation.
For example,
y = 3x + 2.
A function can can also be be written with a mapping arrow.
For example,
x  3x + 2.
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Finding outputs given inputs
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Ordering machines
Is there any difference between
x
×2
+1
y
×2
y
and
x
+1
?
The first function can be written as y = 2x + 1.
The second function can be written as y = 2(x + 1) or 2x + 2.
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Equivalent functions
Explain why
x
+1
×2
y
is equivalent to
x
×2
+2
y
When an addition is followed by a multiplication;
the number that is added is also multiplied.
This is also true when a subtraction is followed by a
multiplication.
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Ordering machines
Is there any difference between
x
÷2
+4
y
÷2
y
and
x
+4
?
x
The first function can be written as y =
+ 4.
2
x+4
x
The second function can be written as y =
or y = + 2.
2
2
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Equivalent functions
Explain why
x
+4
÷2
y
is equivalent to
x
÷2
+2
y
When an addition is followed by a division then the number
that is added is also divided.
This is also true when a subtraction is followed by a division.
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Equivalent function match
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