Key Features of Graphs
I can identify intercepts, max/min points, and increasing/decreasing intervals from a graph.
The problem this sheet solves
Reading a graph is treated as obvious, so the vocabulary never gets pinned down. A maximum is a POINT with two coordinates, not an x-value. Intercepts get named without saying which variable is zero. Increasing and decreasing get read right to left. Each of these produces answers that look close enough to be marked correct and are not. This sheet reads a graph left to right like a sentence and gives each feature a test rather than a description, so students know what counts as an answer. Maxima and minima are required as ordered pairs, intercepts are tied to the variable that equals zero, and intervals are written in terms of x. It covers intercepts, increasing and decreasing, positive and negative, and relative extrema.
The key rule
Read a graph left to right like a sentence: find where it crosses each axis, watch whether it is climbing or falling, and mark the exact point where it turns around.
A turning point is always where increasing switches to decreasing, or the reverse.
Watch out
The mistake: A student reads the maximum of the practice graph as "x = 4" and stops there.
The fix: A max or min is a POINT with two coordinates. "x = 4" throws away the height — the answer is (4, 2).
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.