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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Functions & Graphs: Age 14-16

### Back Fitter

### What's That Graph?

### Surprising Transformations

### Perpendicular Lines

### Negatively Triangular

### At Right Angles

### Doesn't Add Up

### Exploring Cubic Functions

### Parabolic Patterns

### Tangled Trig Graphs

### Functions and Graphs - Short Problems

Y*ou may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.*

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Age 14 to 18

Challenge Level

10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

Age 14 to 18

Challenge Level

Can you work out which processes are represented by the graphs?

Age 14 to 16

Challenge Level

I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?

Age 14 to 16

Challenge Level

Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular lines?

Age 14 to 16

Challenge Level

How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?

Age 14 to 16

Challenge Level

Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?

Age 14 to 16

Challenge Level

In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?

Age 14 to 18

Challenge Level

Quadratic graphs are very familiar, but what patterns can you explore with cubics?

Age 14 to 18

Challenge Level

The illustration shows the graphs of fifteen functions. Two of them have equations y=x^2 and y=-(x-4)^2. Find the equations of all the other graphs.

Age 16 to 18

Challenge Level

Can you work out the equations of the trig graphs I used to make my pattern?

Age 11 to 16

A collection of short problems on straight line graphs.

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