Transform the Inside

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Composition is an operation on functions. It takes two functions and produces a third function.

$(Outside \circ Inside)(d) = Outside(Inside(d))$

For our transformation story, we have a function, $f(x)$ , and we would like to transform horizontally. In a previous section, that has looked like

$f(a \, x + b)$

We can view this as a composition:

$\text {Let } \, L(x) = a \, x + b$

$f(a \, x + b) = (f \circ L)(x)$

Our horizontal graphical transformations can be viewed as a composition with a linear function.

Learning Outcomes

In this section, students will

compose functions with linear functions.

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more examples can be found by following this link
More Examples of Transforming the Inside