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Pdf copy of this post is available here for better formatting and math text.
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Teaching how to sketch a transformed graph of a function requires students to
For most functions and most transformations this hasn't been a major hurdle to deal with. There is, however, one transformation, for one set of functions that has caused me and my students grief every year. And every year I've modified and overhauled how I've taught it to make easier for students. It is horizontal translations for circular functions (sine, cosine, and tangent).
Pdf copy of this post is available here for better formatting and math text.
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Teaching how to sketch a transformed graph of a function requires students to
- know the shape of the untransformed graph
- know key points of the untransformed graph to transform
- know what transformations (dilations, reflections, translations) apply what operations (multiplication, multiplication by negative one, addition) to which variable (x, y)
- know how to determine the transformations from the equation of the function y=f(x) → y=Af(b(x+c))+d
For most functions and most transformations this hasn't been a major hurdle to deal with. There is, however, one transformation, for one set of functions that has caused me and my students grief every year. And every year I've modified and overhauled how I've taught it to make easier for students. It is horizontal translations for circular functions (sine, cosine, and tangent).