Algebra 1 – Unit 3 – Functions





Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, the f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).


Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.


For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.


Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.


Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.


Compare the properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).


Combine standard function types using arithmetic operations.

The “Story” of This Unit

Functions take an input (we call this the domain)…the function “does something” and we get an output (we call this the range). Anything that has a predictable output is called a function, if it doesn’t the input and output are relational, but NOT a function. Understanding what functions are, how they behave and what is considered possible inputs or possible outputs are essential to mathematical thinking. Essentially, we are generalizing possibilities for what could be…and making formal mathematical statements about these possibilities. To make things more complex, we should be able to consider multiple functions and combine them together…the benefit of this is that similar operations only need to be completed once and matters can be made simple. The purpose of learning information in this unit is to understand that functions can make our life more simple, learn how to use functions, learn the “possibilities” of different functions and combine functions to make very complicated things more simple.


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