Relating Ratios and Functions

Relating Ratios and Functions

GCSE(F),

A ratio can be turned into a function. To turn a ratio into a function, one side of the ratio must be set to 1. A ratio of 3 : 7 can be turned into a ratio of 1 : `frac(7)(3)`.

With one side of the ratio set to 1, it can now be mapped as `x -> frac(7)(3)x`, or described as `f(x) = frac(7)(3)x`. The function can be drawn as a graph to show, for example, conversion rates between units (miles and kilometres) or currencies.

The gradient of the graph gives the ratio. The graph will also pass through (0,0).

Examples

1. A ratio 1 : 5 is mapped as a function, and plotted onto a graph. What is the gradient of the graph?.

Answer: 5

The function will be plotted as `x -> 5x`. The gradient is given by `frac(text(up))(text(along))` = `frac(5)(1)`.

2. A courier company charges a flat rate of £10, then £1.20 per kilometre. Can this be written as a ratio? Explain your answer.

Answer: No. When one value of a ratio is zero, then all values of the ratio are zero.

If the charges were plotted as a graph against distance, the graph would not pass through the origin (0,0). This is not a ratio.