Mississippi Math A3.G.39

MathGrades 9–12Geometry (G) Recognize, Sketch, and Transform Graphs to Functions

The Standard

Explain the effects of changing the parameters in transformations of functions.

2025 Mississippi College- and Career-Readiness Standards for Mathematics · Prove and Apply Trigonometric Identities

Teacher's field guide

What Students Need to Do: Students compare a function’s graph before and after a number in its rule changes. They explain how the change shifts, stretches, compresses, or reflects the graph. For sine and cosine, they also describe changes in amplitude and period.
What Mastery Looks Like: Given a sine rule, students can identify its amplitude, period, and shifts, then sketch one cycle. They can explain why multiplying x by 2 halves the period, while adding 1 outside the function moves the graph up.
Common Misconceptions: Students may say that multiplying x by 2 doubles the period. They may move a graph left for (x - 2) or mistake a vertical shift for a change in amplitude.
How to Assess It: Exit ticket: Compare y = sin x with y = 2sin(2(x - π/4)) + 1. Name the new graph’s amplitude, period, and shifts, then sketch one cycle.

Lesson moves

On tracing paper, plot y = sin x, y = 2sin x, and y = sin x + 1 in different colors; label each change.
Show y = sin x beside y = sin(2x); ask, 'Why does the second graph repeat sooner?'
Give pairs cards with sine rules and graphs; have them match each rule to a graph using peaks and zeros.
Plot Ferris wheel models y = 8sin t + 14 and y = 12sin t + 14; ask how radius changes the height range.

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