Lesson Plan

Define the inverse of a function as the rule that reverses its input-output pairing, and explain why $f^{-1}$ does not mean $\frac{1}{f}$

Find $f^{-1}(x)$ for a linear function by swapping $x$ and $y$ and solving for $y$, and explain why the swap comes first

Verify a claimed inverse by composing in both orders and obtaining $x$, and reject a claim when a composition fails

Sketch $f^{-1}$ by reflecting the graph of $f$ across the line $y = x$, using the point rule $(a,b) \mapsto (b,a)$

State the domain and range of $f^{-1}$ from those of $f$

Decide whether a function has an inverse function by applying the horizontal line test, and explain what the test is checking

G 607. Find the coordinates of a point reflected across a vertical or horizontal line or across y = x A 601. Manipulate expressions and equations A 403. Solve routine first-degree equations F 604. Evaluate composite functions at integer values F 707. Exhibit knowledge of logarithms F 505. Understand the concept of a function as having a well-defined output value at each valid input value