Comparing Functions Across Representations
I can compare two functions' rate of change or y-intercept, even shown in different forms.
The problem this sheet solves
Comparing functions fails when students compare whatever is VISIBLE rather than the same property in each form. In an equation the rate of change is already written down; in a table it has to be computed from two rows; on a graph it has to be counted. A student who does not know which is which ends up comparing a slope to a y-value and getting a confident answer. This sheet asks for the same property from each representation before any comparison is made, which turns the task into two extractions and a comparison rather than a guess. Graphs, tables and equations are paired every way round, and rate of change from a table is always calculated across rows so it can never be read off a single cell.
The key rule
To compare two functions in different forms, find the same property in each one — a rate of change or a y-intercept reads the same way no matter which picture it comes from.
Same question, different picture.
Watch out
The mistake: A student sees Function A: y = 2x + 1 and a table for B, then compares "2" straight to a single y-value in B's table.
The fix: The 2 in y = 2x + 1 already IS the rate of change. From a table, a rate of change has to be calculated — change in y over change in x between two rows, not read off one cell.
What is included
- Reference page — student-friendly definitions, a worked example, a Watch Out error pair, and the key rule
- Practice page — six problems, building from foundational to multi-step
- Apply page — a word problem, a reasoning prompt, and an error-analysis task
- Assess — a half-page exit ticket, two to a sheet, with a score box
- Full answer key — every item worked, plus a grading guide that says what each wrong answer tells you
- Ink-saver edition of all 7 pages
- 14-slide teacher deck (PowerPoint) with presenter notes on every slide
Standard codes refer to the Common Core State Standards for Mathematics. Math Class 678 is an independent publisher, not affiliated with, sponsored by, or endorsed by NGA Center or CCSSO. Every product is sold on Teachers Pay Teachers.