The Views of a function exercise appears under the 8th grade (U.S.) Math Mission, Mathematics I Math Mission, Algebra I Math Mission and Mathematics II Math Mission. This exercise emphasizes interchangeability between various forms of a function.

Types of Problems

There are three types of problems in this exercise:

  1. Use the table to make the graph: This problem provides a table and asks the user to graph the points correctly on the coordinate plan.

    Use the table to make the graph

  2. Use the graph to make a table: This problem provides a graph and asks the user to recognize and state several points that are on the graph.

    Use the graph to make a table

  3. Use the rule to make a table: This problem provides a function as an {f(x)} rule and asks users to find several points that satisfy the function.

    Use the rule to make a table


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

  1. A function can be represented in many forms, but the most important idea is that is an assignment of an output to an input. This fact can help to read graphs and follow function rules.
  2. The three major ways to represent most mathematical concepts are via Numerical, Algebraic and Graphical methods. The chart is numerical and the rule is algebraic. The graph is clearly graphical.

Real-life applications

  1. These types of problems can show up on SATs and other standardized tests.
  2. Models, often represented by functions, are developed in many business and science fields. Being able to understand the purpose of a model helps to use them efficiently and accurately.

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