Transformations & asymptotes

Translations, reflections and stretches of graphs, including reciprocal and linear rational functions with vertical and horizontal asymptotes.

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Linear Transformations

Linear transformations of graphs and points: translations by a vector (ab), vertical and horizontal stretches y=af(x) and y=f(qx), vertical and horizontal translations y=f(x)+b and y=f(x−a), and reflections in the x- and y-axes.

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Rational functions

The reciprocal function f(x)=x1, its undefined value at x=0, self-inverse property, and the vertical and horizontal asymptotes of linear rational functions f(x)=cx+dax+b.

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Transformations & asymptotes

Translations, reflections and stretches of graphs, including reciprocal and linear rational functions with vertical and horizontal asymptotes.

Sign up to view your learning progress

Sign up

Learning path

Follow the recommended order, or open any concept.

Start Here

Linear Transformations

Linear transformations of graphs and points: translations by a vector (ab), vertical and horizontal stretches y=af(x) and y=f(qx), vertical and horizontal translations y=f(x)+b and y=f(x−a), and reflections in the x- and y-axes.

0/0 key exercises

Rational functions

The reciprocal function f(x)=x1, its undefined value at x=0, self-inverse property, and the vertical and horizontal asymptotes of linear rational functions f(x)=cx+dax+b.