WTMaths logo
Plot and Interpret Reciprocal Graphs

Plot and Interpret Reciprocal Graphs

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).

Example 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.


Day 0 4 8 12 16 20
Leaves 18 000 3 600 2 000 1 384 1 058 857

Recipricol graph of leaves falling from tree

Example 2

Using the graph in question 1, estimate how many days will elapse until there are only 5,000 leaves left on the tree.

Draw a line along from 5,000 to meet the curve, then read down to 2.6 days.

Answer: 2.6

See also Graphing Reciprocal Functions and Growth and Decay