The opening units of secondary algebra usually cushion students with familiar ground. Simplifying expressions and isolating $x$ in linear equations feel like natural extensions of middle school math. Unit 3 strips away that comfort zone. It introduces relations and functions, demanding that learners treat mathematical entities as relationships rather than dead ends on a single number line.
Gina Wilson’s curriculum introduces the vertical line test early in this packet, prompting students to determine whether a given graph represents a function. Most students memorize the physical act: drag a pencil across the coordinate plane from left to right. If the pencil touches two points at once, the relation fails.
The trouble starts when the study guide presents relations as sets of ordered pairs, mapping diagrams, and discrete tables containing duplicate $x$-values paired with identical $y$-values. Students often freeze when asked whether $\{(2, 5), (3, 7), (2, 5)\}$ is a function. Because they see the number 2 twice, they flag it as a violation, missing that identical coordinates represent the exact same point in Euclidean space. The curriculum deliberately exposes whether a student understands the true definition of a function, that every individual input maps to exactly one output, or is merely executing an unexamined visual trick.
