Florida B.E.S.T. MA.912.F.2.3
The Standard
Given the graph or table of f(x) and the graph or table of f(x)+k,kf(x), f(kx) and f(x+k), state the type of transformation and find the value of the real number k.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students compare a function with a changed version shown in a graph or table. They decide whether inputs or outputs were shifted, scaled, or reflected. They use corresponding values to find k.
What Mastery Looks Like
- Students can match corresponding points and tell whether inputs or outputs changed. They correctly name the shift, stretch, compression, or reflection and calculate k, including negative and fractional values.
Common Misconceptions
- Students often reverse the direction of horizontal shifts, saying f(x+3) moves right. They may confuse f(kx) with a vertical scale change. They may notice a reflection for negative k but miss the related stretch or compression.
How to Assess It
- Exit ticket: f contains (1,2) and (3,4), while g contains (1,6) and (3,12). Write g in terms of f, name the transformation, and find k.
Lesson moves
Ways to Teach It
Place coordinate cards for f on a floor grid, then move each card using a transformation rule and compare the coordinates.
Ask students to explain why f(x+3) moves left while f(x)+3 moves up, using one point as evidence.
Run a card sort matching base graphs, transformed graphs, equations, transformation names, and k values.
Use a daily temperature graph to model a time shift with f(x+k) and a sensor adjustment with f(x)+k.
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Related Standards
- MA.912.F.2.1
Identify the effect on the graph or table of a given function after replacing f(x) by f(x)+k,kf(x), f(kx) and f(x+k) for specific values of k.
- MA.912.F.2.4
Given the graph or table of values of two or more transformations of a function, state the type of transformation and find the values of the real number that de...
- MA.912.F.2.2
Identify the effect on the graph of a given function of two or more transformations defined by adding a real number to the x- or y- values or multiplying the x-...
- MA.912.F.2.5
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 rea...
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