Compare features of functions

The  exercise appears under the Algebra II Math Mission. This exercise practices comparing various features between two functions, each represented in a different way.

Types of Problems
There is one type of problems in this exercise:


 * 1) Answer the question about the functions: This problem provides three functions in rule, table and graphical forms. The student is asked to answer a single question that compares the three functions. It may ask about the x or y-intercept, minimum, or maximum values.Compare features of functions.PNG

Strategies
Knowledge of the graphical and rule use of functions would help to ensure successful completion of this exercise.
 * 1) The y-intercept is the highest an object reaches if it starts going down without any increase or the starting point if it starts going up without any decrease.
 * 2) The x-intercept is the horizontal movement of an object.
 * 3) The vertex of a parabola occurs at the x-value of $$\frac{-b}{2a}$$.
 * 4) When there is a graph provided, the graph is drawn to scale and can be used to find answers instead of necessarily finding equations.

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.