## Essential QuestionWhat is a function? Enduring Understanding Functions have three parts: (i) a domain, which is the set of inputs to the function, (ii) a range, which is the set of outputs, and (iii) some rule or statement of correspond indicating how each input determines a unique output.
The domain and rule of correspondence determine the range.
Graphs are geometric representations of functions.
Functions are equal if and only if they have the same domain and rule of correspondence.
Function notation provides an efficient way to talk about functions, but notation is just that, an efficient way to talk about functions. The variables used to represent domain values, range values, and the function as a whole is arbitrary. Changing variable names does not change the function.
Logical equivalence is a concept that applies to the form of a conditional statement. Every conditional statement and its contrapositive are logically equivalent. Given a true conditional statement, whether the converse or inverse of the conditional statement is also true depends on the content of the statement. The converse and inverse forms are not logically equivalent to the original conditional form.
The definitions of even and odd symmetry for functions are stated as algebraic conditions on values of functions, but each symmetry has a geometric interpretation related to reflection of the graph through one or more of the coordinate axes.
For any graph, rotational symmetry of 180 degrees about the origin is the same as point symmetry of reflection through the origin. |