Families of Functions

When we wish to describe a particular function, we specify its input-output rule. We can do this in a number of ways. For example, if we wish to describe the volume of water in our bathtub, we might:

  • Explain the behavior in plain language:

    "The volume starts (when t = 0 seconds) at V = 0 gallons, then increases at a constant rate of 0.5 gallons per second."

  • Write down an equation:

    V(t) = 0 + (0.5)t

  • List a table of values:

  • Draw a graph:

    Each of these descriptions is a representation of the function that we are trying to model.

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