8.D.1 — Identify functions from mappings, tables, and graphs.
Step 01 of 04
A function is a rule that assigns each input EXACTLY ONE output. The defining property: no input is paired with two different outputs.
"Each x goes to exactly one y" — that's the test.
Step 02 of 04
From a table. Look for any x value that appears twice with DIFFERENT y values.
| (1, 5), (2, 7), (3, 9) | →function (each x unique) |
| (1, 5), (2, 7), (1, 9) | →NOT a function (x = 1 appears twice with different y) |
| (1, 5), (2, 7), (1, 5) | →function (x = 1 maps to same y both times) |
Step 03 of 04
From a graph — vertical line test. Draw any vertical line through the graph. If it hits the curve more than once, NOT a function.
| →parabola — vertical line hits at most once → function | |
| →circle — vertical line through middle hits at TWO points → NOT a function | |
| Straight line (non-vertical) | →function |
| Vertical line itself | →NOT a function (one x, infinite y) |
Step 04 of 04
From a mapping diagram (input arrows pointing to outputs): every input must have exactly one arrow leaving it. Multiple inputs CAN map to the same output (that's allowed); a single input can't map to multiple outputs.
Key insight
Function = each input has EXACTLY ONE output. Test from a table (no duplicate x with different y), graph (vertical line test), or mapping (each input one arrow out).