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Comparing linear functions
Comparing-features-of-functions-0-5 256
Description
Exercise Name: Comparing linear functions
Math Missions: 8th grade (U.S.) Math Mission, Algebra I Math Mission
Types of Problems: 5

The Comparing linear functions exercise appears under the 8th grade (U.S.) Math Mission and Algebra I Math Mission . This exercise finds points of comparison between various linear functions.

Types of Problems

There are five types of problems in this exercise:

  1. Determine which function is changing faster: This problem provides two functions in different forms. The student is asked to determine which is increasing or decreasing faster.
    Clf1

    Determine which function is changing faster

  2. Find the line with the same slope: This problem provides a graph with several lines. The student is asked to determine which graph has the same slope as the given function.
    Clf2

    Find the line with same slope

  3. Figure out which function gets to a value faster: Instead of looking for a slope, this problem asks which function arrives at a certain output faster. The student selects the correct answer from a multiple choice list.
    Clf3

    Figure out which function gets to a value faster

  4. Determine all lines that increase faster: This problem is much like another problem, but in this case there is a multiple select list to provide the possibility that more than one function would work.
    Clf4

    Determine all lines that increase faster

  5. Determine information about intercepts: This problem provides two functions in different forms. The student is asked to determine which has the larger intercept.
    Clf5

    Determine information about intercepts

Strategies

Knowledge of the various forms of lines and many forms of functions are a great advantage to doing this exercise accurately and efficiently.

  1. Knowing how to interpret slope and intercepts from graphs, charts and rules are a great advantage for speed.
  2. Problems could change decreasing for increasing and higher for lower in the future, so it is important to read carefully before answering.

Real-life applications

  1. Lines have many applications in business and the sciences.
  2. Intercepts tend to be initial conditions, and slope is the marginal cost to create more items.
  3. 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.
  4. 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.
  5. 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.

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