The Recognizing functions from graphs exercise appears under the Mathematics I Math Mission, 8th grade (U.S.) Math Mission, Algebra I Math Mission, Mathematics II Math Mission, Algebra II Math Mission and Mathematics III Math Mission. This exercise begins to recognize what makes a relation a function.

Types of Problems

There are two types of problems in this exercise:

  1. Determine if word problem represents a function: This problem describes a situation in context. The user is expected to determine if the problem describes a situation that could be modeled with a function.

    Determine if the word problem represents a function

  2. Determine if drawing is a function of either variable: This problem has provides the graph of a relation. The user is asked to determine if the graph is {x} as a function of {y}, {y} as a function {x}, neither, or both.

    Determine if drawing is a function of either variable


Knowledge of function notations and the various forms of functions are an advantage when trying to complete this exercise.

  1. A function must be assigned a unique output for any input.
  2. For graphical situations, a graph is a function of {y} in terms of {x} if it passes the vertical line test. It is a function of {x} in terms of {y} if it passes the horizontal line test.

Real-life applications

  1. Functions are the building blocks of much of the calculus.
  2. Functions can be used to model many aspects of business and science.

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