Interpreting graphs
When reading and interpreting graphs it is important to carefully consider what each axis represents. You may also need to take a general approach as you will not always be given specific values to work with.
Question
The following shapes are filled with water, where the water is poured at a constant rate. The graphs model the height of water against time. Match up the correct graph to each shape.
- A. The height of the water increases at a constant rate. This applies to shapes 1 and 4.
- B. The height increases quickly and then slows down. This applies to shapes 3 and 5. As the water level rises, there is a larger area to cover and therefore the height increase will slow down.
- C. The height increases slowly, quickly and then slowly again. This applies to shape 2, we can see that after a non-uniform decrease in the diameter the shape is at is narrowest and therefore in this part the height of the water will increase more rapidly than in other parts.
Question
At a company, employees receive £200 commission even if they sell nothing, plus 1% for all sales made under £20,000 and 4% for all sales over £20,000. Which graph best represents this scenario?
Graph C. There is a payment irrespective of sales of £200, so the graph can’t start at (\({0} \text{,} {~0}\)). For sales over £20,000, the percentage received increases, so the gradient of the line should also increase.