Mississippi Math FA.F.21
The Standard
Describe the following characteristics of linear and quadratic parent functions by inspection: domain/range, increasing/decreasing intervals, intercepts, symmetry, and asymptotic behavior. Identify each characteristic in set notation or words, where appropriate. (A3.A.8)
2025 Mississippi College- and Career-Readiness Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students inspect the graphs of y=x and y=x² to find their domains, ranges, intercepts, intervals of increase or decrease, and symmetry. They describe what each graph does far to the left and right, and check whether it approaches an asymptote.
What Mastery Looks Like
- Both domains and the range of y=x are all real numbers. The range of y=x² is y≥0. Students locate both intercepts at (0,0), identify where each graph increases or decreases, name each graph’s symmetry, and recognize that neither has an asymptote.
Common Misconceptions
- Students may give y=x² a negative range because its graph includes negative x-values. Some say it increases everywhere because both ends rise. Others mistake the y-axis for an asymptote or give y=x the same symmetry as y=x².
How to Assess It
- Exit ticket: Sketch y=x and y=x². For each graph, list its domain, range, intercepts, intervals of increase or decrease, symmetry, and any asymptotes. Write what happens at each end.
Lesson moves
Ways to Teach It
Plot y=x and y=x² on graph paper, then use tracing paper to test each graph for reflection and half-turn symmetry.
Ask, “Why can x be negative for y=x² but y cannot?” Have students explain using x=−2.
Give pairs cards showing graph features to match with y=x, y=x², or both, then defend one match.
Sketch a tossed ball’s height over time, then compare its limited time domain and line of symmetry with y=x².
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- FA.F.19
Create and identify the parent function for linear and quadratic functions in the Coordinate Plane.
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