Inverse functions and graph transformations

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Determine whether a function is one-to-one on a stated domain and explain when an inverse exists.
Find inverse functions algebraically and state any necessary domain or range restrictions.
Verify inverse relationships using composition.
Sketch or interpret the graph of an inverse function as a reflection in the line $y=x$.

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Relate algebraic forms such as $y=f(x)+a$, $y=f(x+a)$, $y=af(x)$ and $y=f(ax)$ to their graph transformations.

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