Transformations of Linear Functions
I can describe and write the result of shifting, stretching, or reflecting a linear function.
The problem this sheet solves
Inside the bracket, transformations run backwards, and no amount of stating that fixes it, because the symbol is right there contradicting the rule. Students also mix up which changes affect input and which affect output, so vertical and horizontal shifts get swapped along with their directions. This sheet separates outside from inside as a first sort, then settles direction by TESTING A POINT rather than by recall, which is a method a student can use when the rule has gone. Shifts, stretches and reflections are practised together so the sort has to be made every time.
The key rule
Outside the bracket moves the OUTPUT. Inside it moves the INPUT, and reverses: f(x − h) moves RIGHT h. When in doubt, test a point.
Inside the bracket goes the other way.
Watch out
The mistake: A student says f(x − 3) moves the graph 3 to the LEFT, because of the minus sign.
The fix: Test a point. f(0) = 1, and g(3) = 1 as well. The output that used to appear at x = 0 now appears at x = 3, so the graph moved RIGHT 3.
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.