### There are 14 results

Broad Topics >

Sequences, Functions and Graphs > Functions and their inverses

##### Age 16 to 18 Challenge Level:

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

##### Age 16 to 18 Challenge Level:

Which curve is which, and how would you plan a route to pass between them?

##### Age 16 to 18 Challenge Level:

By sketching a graph of a continuous increasing function, can you prove a useful result about integrals?

##### Age 16 to 18 Challenge Level:

Can you make a curve to match my friend's requirements?

##### Age 16 to 18 Challenge Level:

Consider these questions concerning inverting rational functions

##### Age 16 to 18 Challenge Level:

When can a pdf and a cdf coincide?

##### Age 16 to 18 Challenge Level:

Can you match these equations to these graphs?

##### Age 16 to 18 Challenge Level:

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.

##### Age 16 to 18 Challenge Level:

Make a functional window display which will both satisfy the manager and make sense to the shoppers

##### Age 16 to 18 Challenge Level:

A function pyramid is a structure where each entry in the pyramid is determined by the two entries below it. Can you figure out how the pyramid is generated?

##### Age 16 to 18 Challenge Level:

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

##### Age 14 to 16 Challenge Level:

Place a red counter in the top left corner of a 4x4 array, which is
covered by 14 other smaller counters, leaving a gap in the bottom
right hand corner (HOME). What is the smallest number of moves. . . .

##### Age 16 to 18 Challenge Level:

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

##### Age 16 to 18 Challenge Level:

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.