The main object of study for this week (as well as for all of Algebra) is the Function. A function “f” is a correspondence between two sets, the domain of the function, x, and the range of the function, f(x) such that every element x of the domain corresponds with exactly one element y, or f(x), of the range.
In this week’s Algebra Talk, we will discuss the concept of a function along with some properties and examples. Please start by addressing one or more of the following topics to get the discussion going:
1. Give an example from real life where functions are utilized. For ideas, look it up on the internet or find some examples in the textbook. Why did you pick this example? How might you or your classmates use this in the future?
2. If the domain and range of a function consists of real numbers, then you can graph it by plotting all ordered pairs of the form (x, f(x)). How can you tell by looking at a graph if it represents a function?
3. What is meant by a “piecewise-defined” function? Give a real-world example or an example using real numbers.
Example: Here is a real-world example to help you explain what a piecewise-defined function is and to give other examples:
At a local pizza restaurant, it costs $15 for a cheese pizza. However, if you buy more than 5 pizzas, it only costs $12 per pizza. Thus, the cost of a pizza is given by the following piecewise-defined function:
4. Why are there usually two solutions in quadratic equations?
5. Give an example from real life where quadratics are utilized. For ideas, look it up on the internet or find examples in the textbook. Why did you pick this example?