# Functions and Graphs - Stage 3

Scroll down to see our complete collection of problems on functions and graphs, or explore the two sub-collections focussing on different aspects of functions and graphs.

### Straight Line Graphs

These problems will require you to consider the gradients, intercepts and equations of straight line graphs.

### Using Graphs

These problems will require you to consider practical contexts in which graphs can be used.

### How Far Does it Move?

##### Age 11 to 14Challenge Level

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.

### Speeding Up, Slowing Down

##### Age 11 to 14Challenge Level

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.

### Up and Across

##### Age 11 to 14Challenge Level

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its vertical and horizontal movement at each stage.

### Route to Infinity

##### Age 11 to 14Challenge Level

Can you describe this route to infinity? Where will the arrows take you next?

### Parallel Lines

##### Age 11 to 14Challenge Level

How does the position of the line affect the equation of the line? What can you say about the equations of parallel lines?

### Diamond Collector

##### Age 11 to 16Challenge Level

Collect as many diamonds as you can by drawing three straight lines.

### Treasure Hunt

##### Age 7 to 14Challenge Level

Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?

### Maths Filler

##### Age 11 to 14Challenge Level

Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?

### Reflecting Lines

##### Age 11 to 14Challenge Level

Investigate what happens to the equations of different lines when you reflect them in one of the axes. Try to predict what will happen. Explain your findings.

### Translating Lines

##### Age 11 to 14Challenge Level

Investigate what happens to the equation of different lines when you translate them. Try to predict what will happen. Explain your findings.

### How Steep Is the Slope?

##### Age 11 to 14Challenge Level

On the grid provided, we can draw lines with different gradients. How many different gradients can you find? Can you arrange them in order of steepness?

### Fill Me Up

##### Age 11 to 14Challenge Level

Can you sketch graphs to show how the height of water changes in different containers as they are filled?

### Lattice Points on a Line

##### Age 11 to 14 ShortChallenge Level

How many lattice points are there in the first quadrant that lie on the line 3x + 4y = 59 ?

### Graph Area

##### Age 11 to 14 ShortChallenge Level

Can you find the area between this graph and the x-axis, between x=3 and x=7?

### Point in Between

##### Age 11 to 14 ShortChallenge Level

Find the point on the line segment AB that is twice as far from B as it is from A.

### Linear Area

##### Age 11 to 14 ShortChallenge Level

Find the area of the triangle enclosed by these lines.