## 1.4 Analysing Non-Linear Graphs

### Intercepts of Non-Linear Graphs

- Non-linear graphs can have
**no**intercepts,**one i**ntercept or**multiple**intercepts along either axis.

Example

Above is a graph showing the profits earned by a community theatre in the years before they changed management. In the context of this situation, we can say that the intercepts at t=-3, -2 and 1 years represent points at which the community theatre just broke even (i.e. no profit or loss). The intercept at P=$1000 represents the profits made in the year the new management took over.

### Maximum/Minimum Points

- It may interest us to know the highest, or lowest values that the y-variable has taken. For example, if we want to find the highest a tide has been in a year in order to know how high to build a support structure.
- The
**maximum**and**minimum points**of non-linear graphs will be points of**0 gradient**or the**endpoints**of a section (i.e. where a graph ends or undergoes structural change). - There may be multiple minimum points and/or multiple maximum points.