The Evaluate composite functions from graphs and tables exercise appears under the Algebra II Math Mission and Mathematics III Math Mission. This exercise practices evaluating the composition of those functions at a given inputs given the graphs, or some tables of values, of two functions.

Types of Problems[]

There are two types of problems in this exercise:

  1. Which of the following best approximates the value of ___?: This problem provides the graph of two functions and an expression using those two functions. Then, user is expected to correctly evaluate the expression below and write the correct answer in the space provided.

    Find Which of the following best approximates the value of ___.

  2. Evaluate the expression.: This problem provides tables below that shows some inputs and outputs of functions ___ and ___. Then, user is expected to correctly evaluate the expression below and write the correct answer in the space provided.

    Evaluate the expression.

Strategies[]

Knowledge and experience with composite functions would help to ensure success on this exercise.

  1. When evaluating composite functions, users should work our way inside out.
  2. The final answer submitted will be an integer.

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.

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