# 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.

##### KS 4 Challenge Level:

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

### Walk and Ride

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

How far have these students walked by the time the teacher's car reaches them after their bus broke down?

### 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.

### 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?

### Perpendicular Lines

##### KS 3 Challenge Level:

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

### Diamond Collector

##### KS 3 Challenge Level:

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

### Negatively Triangular

##### KS 4 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 ?

### Maths Filler

##### KS 4 Challenge Level:

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

### At Right Angles

##### KS 3 Challenge Level:

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

### 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.

### Surprising Transformations

##### KS 3 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?

### 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?

### Exploring Simple Mappings

##### KS 3 Challenge Level:

Explore the relationship between simple linear functions and their graphs.

### 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?

### Functions and Graphs Stage 3 - Short Problems

##### KS 3 & 4

A collection of short Stage 3 and 4 problems on straight line graphs.

### 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 ?