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 vertically. In a previous section, that has looked like
\[ a \, f(x) + b \]
We can view this as a composition:
\[ \text {Let } \, L(x) = a \, x + b \]
\[ a \, f(x) + b = (L \circ f)(x)\]
Our vertical 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 Outside