Mississippi Math A3.G.40

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

The Standard

Predict the shapes of graphs of exponential, logarithmic, rational, and piece-wise functions, and verify the prediction with and without technology.

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

Teacher's field guide

What Students Need to Do: Students predict a graph’s shape from its equation before plotting points. They sketch exponential, logarithmic, rational, and piecewise graphs by hand, then check their sketches with a value table and a graphing tool.
What Mastery Looks Like: Students can sketch a new equation from each family and mark features that apply, such as intercepts, asymptotes, and open or closed endpoints. They use calculated points and a graphing tool to find and fix mistakes.
Common Misconceptions: Students may draw a rational graph through a vertical asymptote or connect two piecewise rules across a jump. They may also plot a logarithm where its input is zero or negative.
How to Assess It: Exit ticket: Sketch y=1/(x−2) and f(x)=x when x<0, f(x)=2 when x≥0. Mark the break in each graph, then check both sketches in Desmos and correct any errors.

Lesson moves

Use graph paper and colored pencils to plot y=1/x from a hand-made value table, leaving x=0 blank.
Ask partners, “Why does y=log₂(x) have no points left of the y-axis, while y=2^x does?”
Play graph bingo: show equations for four function families, have students mark matching sketch cards, then check answers in Desmos.
Sketch a $100 balance growing 5% yearly, then compare calculated balances for years 0, 1, and 2 with a graphing calculator.

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