Counterexample : A counterexample to a statement of the form 'all objects of type x have property y' is an object of type x that does not have property y. A counterexample to a statement shows that the statement is not true in general. For example the number 3 is a counterexample to the statement that all numbers are even.

Function : A function is a mapping in which every element in one set is mapped to exactly one element of a second set. Most often the mapping is described using a rule. For example the function $f(x)=x+1$ maps 2 to 3 and -1 to 0.

Root : A root is a solution to an equation of the $f(x)=0$ where $f$ is a function or expression. For example the function $f(x)=x-1$ has the root $x=1.$

Function : A function is a mapping in which every element in one set is mapped to exactly one element of a second set. Most often the mapping is described using a rule. For example the function $f(x)=x+1$ maps 2 to 3 and -1 to 0.

Graph : The graph of a function is the set of points $\{(x,f(x))\}$ that can be blotted in a coordinate system.

Expression : An expression is a succession of constants, variables and mathematical operations that if evaluated for specific values of the variables represents a number.

Number : A number $x$ is a mathematical symbol representing a quantity.