How it works
A relation can be shown as a mapping, a table, a graph or an equation, and the test for a function looks different in each. This functions graphic organizer asks for all four on one page, with the reason written under each.
Read the full guide
One test, four looks
In a mapping diagram, look for an input with two arrows leaving it. In a table or a list of ordered pairs, look for an input that appears twice with different outputs. On a graph, use the vertical line test. For an equation, try to find one input that gives two outputs.
Then the notation
Once students can say why a rule is a function, give it a name. The notation box takes one function apart, and the evaluating chart puts six inputs through it.
- Two inputs may share an output. In the third relation of the tick chart every input gives 5, and it is still a function.
- For the equation box, try x = y². The input 4 gives two outputs, 2 and −2, so it is not a function.
Questions and answers
What is a function in math?
A rule that assigns to each input exactly one output. The Common Core standards for grade 8 word it that way, and add that the graph of a function is the set of ordered pairs of an input and its output.
What is the vertical line test?
A way to tell from a graph whether it shows a function. If any vertical line crosses the curve more than once, one value of x has more than one value of y, so the curve is not the graph of a function.
What does f(x) mean?
It stands for the output of the function f for the input x. For f(x) = 2x + 3, f(4) is the output when the input is 4: 2 times 4, plus 3, which is 11.