Evaluating Functions
I can substitute a number into a function rule, signs and all, and tell evaluating from solving.
The problem this sheet solves
Evaluating functions hides two separate errors behind one instruction — "put the number in." The first is the sign: no brackets means a minus sign detaches from the number it belongs to, and −2² quietly becomes −4 instead of 4. The second is deeper and never shows up as a wrong-looking answer: f(7) and "find x when f(x) = 7" are eleven characters apart and opposite operations, and a student who cannot tell them apart just answers the one they recognize — correctly — and loses the mark anyway. This sheet refuses to let either error hide behind the other. Practice 3 and 4 share one rule and one numeral and land on different answers on purpose, so a student who writes the same number twice has told you exactly which half of the skill is missing. The grading guide says to mark in pairs, not by item, because a single question can never separate a sign slip from a direction error — only its neighbor can.
The key rule
To evaluate, put the input in BRACKETS wherever x stood and work it out; the brackets keep a minus sign attached to the number it belongs to. Then check which side the number is on: in f(7) the 7 is going in, and in f(x) = 7 it has already come out.
Brackets every time. Then ask which side the number is on.
Watch out
The mistake: No brackets, so −2² is read as −4 and the answer comes out as 2; or answering f(7) when the x with f(x) = 7 was asked for.
The fix: Bracket it: (−2)² is 4, so f(−2) = 10. And read which side the number sits on before starting.
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.