# 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.

### Coordinate Patterns

##### KS 3 Challenge Level:

Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?

### How Far Does it Move?

##### KS 3 Challenge 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

##### KS 3 Challenge 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

##### KS 3 Challenge Level:

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

### Route to Infinity

##### KS 3 Challenge Level:

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

### Parallel Lines

##### KS 3 Challenge 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

##### KS 3 Challenge Level:

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

### Cops and Robbers

##### KS 2, 3 & 4 Challenge Level:

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

### Maths Filler

##### KS 3 Challenge Level:

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

### Reflecting Lines

##### KS 3 Challenge 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

##### KS 3 Challenge 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?

##### KS 3 Challenge 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

##### KS 3 Challenge 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

##### KS 3 Short Challenge Level:

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

### Graph Area

##### KS 3 Short Challenge Level:

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

### Point in Between

##### KS 3 Short Challenge Level:

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