C. Independent and Dependent Variables

The input values of a relation, often the x-values, are also referred to as the independent variable values. The domain of a relation represents the acceptable values for the independent variable. Similarly, the output values of a relation, which are often the y-values, are referred to as the dependent variable values. The range of a relation represents the acceptable values for the dependent variable.

As such, the horizontal axis of a graph is named after the independent variable of a relation and the vertical axis is named after the dependent variable. The independent variable influences a result. For instance, the length of time spent studying can influence exam results. The dependent variable values are the result of the independent variable's influence. For instance, better exam results occur when study time is increased.

The output ( y-value) of a relation depends on the input ( x-value).

Independent Variable
a variable whose value is not determined by another variable

Dependent Variable
a variable whose value is determined by another (independent) variable

 

Example 1

Identify the independent and dependent variables in the following scenarios. Explain your choices.

  1. The success rate of basketball shots from various distances from the hoop.

    Independent variable - distance from the hoop
    Dependent variable - success rate of the shot
    The success rate of a basketball shot depends on the player's distance from the hoop.

  2. The growth of plants fed different amounts of nutrients.

    Independent variable - amounts of nutrients given to plants
    Dependent variable - growth of the plants
    The growth of a plant depends on the amount of nutrients given.

  3. Fuel consumption at different rates of speed.

    Independent variable - speed
    Dependent variable - fuel consumption
    The amount of gasoline used depends on the speed of a vehicle.