An option payoff diagram is used to illustrate how an option will perform given the movement of the Underlying price. Since option buyers have a defined risk (i.e. they can lose no more than the cost they paid for the option) an option payoff diagram is not a straight diagonal line. Further, combining both Long and Short strategies produces more complex payoff diagrams. The shapes formed by these are where the names of many popular option strategies are derived from, e.g butterflies, iron condors or straddles.
Structure of a Profit and Loss Diagram
Example Payoff Diagrams
Some Options Trading platforms will automatically generate payoff diagrams using an investor's positions so they can see at a glance what effect changing Underlying prices might have.