Florida B.E.S.T. MA.912.F.2.5
The Standard
Given a table, equation or graph that represents a function, create a corresponding table, equation or graph of the transformed function defined by adding a real number to the x- or y-values or multiplying the x- or y-values by a real number.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students change a function’s inputs or outputs by adding or multiplying by a real number. They show the result as a table, equation, or graph and connect coordinate changes to function notation.
What Mastery Looks Like
- Students correctly transform every point and write an equivalent function rule. They explain why changes outside the function affect outputs, while changes inside affect inputs in the opposite direction.
Common Misconceptions
- Students often use the same sign for horizontal shifts, writing f(x+4) for a shift right 4. They may think f(2x) doubles x-coordinates, but it halves them on the graph.
How to Assess It
- Exit ticket: Start with f(x)=x² and the points (0,0), (1,1), and (2,4). Multiply each x-value by 2 and subtract 3 from each y-value, then write g(x) and the transformed points.
Lesson moves
Ways to Teach It
Give pairs coordinate cards and graph paper; students transform every point using (x,y) to (2x,y−3), then connect the new graph.
Students answer the prompt, “Why does f(x+4) move left while f(x)+4 moves up?”, using one test point.
Run a card sort matching base graphs, transformed equations, coordinate rules, and descriptions, with students checking each set using two points.
Give a Celsius temperature table and have students create Fahrenheit outputs by multiplying y-values by 9/5 and adding 32.
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