Lesson Plan

• Define an inverse function and state the one‑to‑one condition required for its existence.
• Sketch a given function and its inverse on the same set of axes.
• Explain why the graphs are mirror images across the line y = x.
• Use reflected points to determine values of the inverse function.
• Check that the inverse graph also satisfies the Horizontal Line Test.

• Projector or interactive whiteboard
• Graph paper and rulers
• Whiteboard and markers
• Worksheet with tables for plotting points
• Calculators (optional)

Begin by asking students what happens when the coordinates of a point are swapped – where does the point move? Review the Horizontal Line Test from the previous lesson. Explain that today they will prove that an inverse function is the reflection of the original graph across the line y = x, and they will be able to sketch both graphs and justify the relationship.

1. Do‑now (5'): Quick quiz on identifying one‑to‑one functions using the horizontal line test.
2. Mini‑lecture (10'): Introduce inverse functions, the reflection principle, and draw the line y = x on the board.
3. Guided demonstration (15'): Teacher sketches f(x)=2x+1, plots several points, reflects them to obtain f⁻¹(x), and labels the axes.
4. Pair activity (15'): Students choose a new function, plot points on graph paper, reflect them, complete the worksheet, and write the algebraic form of the inverse.
5. Check for understanding (5'): Groups share one reflected point and the corresponding inverse value; teacher corrects common errors.

Recap that the inverse graph is a mirror image of the original across y = x and that this visual test confirms the one‑to‑one property. For the exit ticket, each student writes a single sentence describing the reflection relationship. Homework: complete the three practice questions on inverses and submit a neat sketch of each function with its inverse.