Mississippi Math A3.A.8
The Standard
Determine characteristics of graphs of parent functions (domain/range, increasing/decreasing intervals, intercepts, symmetry, end behavior, and asymptotic behavior).
2025 Mississippi College- and Career-Readiness Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students read parent-function graphs to find possible inputs and outputs, intercepts, and where each graph rises or falls. They check symmetry, describe what happens at each end, and identify any asymptotes.
What Mastery Looks Like
- For y=x², students give the domain and range, then name where the graph decreases and increases. For y=1/x, they name no intercepts, identify origin symmetry, and mark both asymptotes. They describe each graph's end behavior and exclude zero from the domain and range of y=1/x.
Common Misconceptions
- Students swap domain and range or include zero in the domain of y=1/x. They call an asymptote an intercept or say y=1/x decreases across x=0, where it is undefined. They may mistake origin symmetry for symmetry about the y-axis.
How to Assess It
- Give students a sketch of y=1/x. Ask them to label its domain, range, intercepts, decreasing intervals, symmetry, asymptotes, and behavior at both far ends.
Lesson moves
Ways to Teach It
Give pairs printed graphs of y=x², y=√x, and y=1/x; students shade each domain and range on number lines and draw any asymptotes.
Ask, 'Why does y=x² rise at both far ends, while y=x³ falls on the left?' Have students write a two-sentence explanation.
Play graph bingo: call out 'symmetric about the y-axis' or 'domain x≥0'; students cover matching parent-function graphs.
Calculate trip times at 10, 20, and 30 mph for 60 miles; sketch time versus speed and discuss why time never reaches zero.
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