Florida B.E.S.T. MA.912.F.2.2
The Standard
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- 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 read a transformed function and describe each horizontal or vertical shift, stretch, compression, or reflection. They write a new function from a sequence of changes and map key points to the new graph.
What Mastery Looks Like
- Given g(x)=-2f(3(x-4))+1, a student identifies right 4, horizontal compression by 1/3, reflection across the x-axis, vertical stretch by 2, and up 1. The student can write an equation from a described sequence and correctly transform key points.
Common Misconceptions
- Students often use the visible sign inside the function, moving f(x-3) left instead of right. They may call f(3x) a horizontal stretch by 3, confuse reflection axes, or apply changes in the wrong order.
How to Assess It
- Exit ticket: For g(x)=-2f(3(x-4))+1, list every graph change and map the point (1,5) from f to g.
Lesson moves
Ways to Teach It
Plot a parent function on tracing paper, then slide, flip, and stretch it over a coordinate grid while recording each new equation.
Compare f(x-3)+2 and 2f(x)-3, then write which changes affect inputs, outputs, and graph location.
Run a card sort matching parent graphs, transformed equations, transformation sequences, and mapped key points.
Use a daily Celsius temperature function to create and graph its Fahrenheit version, then explain the output scale and shift.
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Related Standards
- 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...
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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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Describe and apply the effect of a single transformation on two-dimensional figures using coordinates and the coordinate plane.
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