Summary: Transforming functions

The  exercise appears under the Algebra II Math Mission. This exercise practices with the graphs of functions f and g where g is a transformation of f, determining the formula of g in terms of f.

Types of problems
There is one type of problem in this exercise:
 * 1) What is $$g(x)$$ in terms of $$f(x)$$?: This problem features a graph with functions $$g(x)$$ and $$f(x)$$, and $$g(x)$$ is a transformation of $$f(x)$$. The student is expected to evaluate what $$g(x)$$ is in terms of $$f(x)$$.

Strategies
Basic knowledge of transforming functions is required for this exercise.


 * 1) When a function is shifted, stretched (or compressed), or flipped in any way from its "parent function", it is said to be transformed, and is a transformation of a function.  Functions are typically transformed either vertically or horizontally.
 * 2) T-charts are extremely useful tools when dealing with transformations of functions.

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.