The Evaluating functions 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 gives understanding of how functions work as input-output machines.

Types of Problems

There are two types of problems in this exercise:

  1. Find the value from the graph: This problem provides a graph and asks users to find the output for a particular input for the graphed function.

    Find the value from the graph

  2. Find the value from the rule: This problem provides a rule for calculating a function. The user is asked to find the output for a particular input.

    Find the value from the rule


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.

Real-life applications

  1. Money as a function of time. One never has more than one amount of money at any time because they can always add everything to give one total amount. By understanding how their money changes over time, they can plan to spend their money sensibly. Businesses find it very useful to plot the graph of their money over time so that they can see when they are spending too much.
  2. Temperature as a function of various factors. Temperature is a very complicated function because it has so many inputs, including: the time of day, the season, the amount of clouds in the sky, the strength of the wind, and many more. But the important thing is that there is only one temperature output when they measure it in a specific place.
  3. Location as a function of time. One can never be in two places at the same time. If they were to plot the graphs of where two people are as a function of time, the place where the lines cross means that the two people meet each other at that time. This idea is used in logistics, an area of mathematics that tries to plan where people and items are for businesses.
  4. Calculus describes how function change and experience with analysis of graphs will increase ability in calculus.
  5. These types of problems can show up on SATs and other standardized tests.
  6. 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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