Plot and Interpret Reciprocal Graphs

# Plot and Interpret Reciprocal Graphs

GCSE(F), GCSE(H),

To plot a reciprocal graph, use several points. A reciprocal graph will have two lines, and both lines will be curved and tend toward the asymptotes. In real-life situations, only the positive part (above the x-axis) of the graph is shown. In algebraic usage, the negative part, which will be partially or totally below the y-axis, may also be shown.

Reciprocal graphs tend to show efficiency (fuel used against speed, the number of people allocated to a task against the time taken to complete it), or growth/decay (half-life of a radioactive sample).

## Examples

1. A tree loses its leaves in inverse proportion to time: early in Autumn it loses many per day; later in Autumn it loses only a few per day. The function can be modelled using: frac(s)(d + 1), where s is the number of leaves on the tree at the start of Autumn and d is the number of days into the season.

Plot the graph for 20 days into the season, where the initial number of leaves was 18 000.

2. Using the graph in question 1, estimate how many leaves will still be on the tree after 9 days.