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## 'Exploring Simple Mappings' printed from http://nrich.maths.org/

Ed from St Peters College noticed
that:
If the numbers aren't changed ($\times2$ and $+3$), the final
answer will always be odd.

When the values of the $2$ and $3$ are changed, from an even and an
odd, to an odd and an even, the answer will be the same type as the
number placed in the input box at the start:

if the input is even, the answer
will be even

if the input is odd, the answer
will be odd

Thomas from Wilson's School noticed
that:

The higher the numbers you are multiplying by, the steeper the
gradient of the graph.

The addition or subtraction determines where the graph cuts
the y-axis.

Rajeev from Fair Field Junior School
in Radlett summarised his findings clearly here
He started to consider the equations
of perpendicular lines. You can go to Perpendicular
Lines if you would like to explore this
further.