# Functions & Graphs: Age 14-16

This is part of our Secondary Curriculum collection of favourite rich tasks arranged by topic. ### Back Fitter

##### Age 14 to 16 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? ### What's That Graph?

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

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

##### 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? ### Perpendicular Lines

##### 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? ### Negatively Triangular

##### 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 ? ### At Right Angles

##### 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? ### Exploring Cubic Functions

##### Age 14 to 18 Challenge Level:

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

##### 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. ### Tangled Trig Graphs

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

Can you work out the equations of the trig graphs I used to make my pattern? ### Functions and Graphs - Short Problems

##### Age 11 to 16

A collection of short problems on straight line graphs. You may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.