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Recognizing functions from tables
Recognizing functions 256
Description
Exercise Name: Recognizing functions from tables
Math Missions: 8th grade (U.S.) Math Mission, Algebra I Math Mission, Mathematics II Math Mission
Types of Problems: 3

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

Types of Problems

There are three types of problems in this exercise:

  1. Use the vertical or horizontal line test: This problem has a graph and the user is expected to look at the graph and determine if one variable is a function of the other.
    Rf1

    Use the vertical or horizontal line test

  2. Solve to see if an equation is a function: This problem provides an equation and asks users to state whether or not it represents a function.
    Rf2

    Solve to see if an equation is a function

  3. See if chart is a function: This problem provides a chart and asks users to determine if the chart represents a function.
    Rf3

    See if chart is a function

Strategies

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.
  3. In a chart, a function will not have repeated x-values going to different y-values.
  4. In a rule, a function can be isolated for y.

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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