Functions and their inverses

What is happening at each box in these machines?

Decipher a simple code based on the rule C=7P+17 (mod 26) where C is the code for the letter P from the alphabet. Rearrange the formula and use the inverse to decipher automatically.

Crack this code which depends on taking pairs of letters and using two simultaneous relations and modulus arithmetic to encode the message.

Plot the graph of x^y = y^x in the first quadrant and explain its properties.

We only need 7 numbers for modulus (or clock) arithmetic mod 7 including working with fractions. Explore how to divide numbers and write fractions in modulus arithemtic.

Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?

Here are several equations from real life. Can you work out which measurements are possible from each equation?

Can you match these equations to these graphs?