• recognize a relationship as a function when each input is assigned to exactly one unique output;
• reason from a context, a graph, or a table, after first being clear which quantity is considered the input and which is the output;
• produce a counterexample: an “input value” with at least two “output values” when a relationship is not a function;
• explain how to verify that for each input there is exactly one output; and
• translate functions numerically, graphically, verbally, and algebraically.
“Function machine” representations are useful for helping students imagine input and output values, with a rule inside the machine by which the output value is determined from the input. Notice that the standards explicitly call for exploring functions numerically, graphically, verbally, and algebraically (symbolically, with letters). This is sometimes called the “rule of four.”