Lesson Plan

• Describe how the graph of y = |f(x)| is obtained from y = f(x) for linear, quadratic, cubic and trigonometric functions.
• Explain why points where f(x) < 0 are reflected in the x‑axis and identify the resulting shape changes.
• Apply a piece‑wise definition to sketch and analyse |f(x)| for given functions.
• Identify the “kinks’’ that occur at the original x‑intercepts of f(x) after applying the absolute‑value operation.
• Use the concept of |f(x)| to calculate areas between a curve and the x‑axis on intervals where f(x) is negative.

• Projector and screen
• Whiteboard and markers
• Graphing calculators (or computer with GeoGebra/Desmos)
• Worksheet with practice questions and space for sketches
• Graph paper and coloured pencils
• Exit‑ticket slips

Begin with a quick visual of a line crossing the x‑axis and ask students what happens if we take the absolute value of its y‑coordinates. Review the idea that |·| makes all numbers non‑negative. State that by the end of the lesson they will be able to transform any f(x) graph into |f(x)| and explain the changes.

1. Do‑Now (5 min): Sketch y = mx + b and mark where f(x) < 0. Share answers.
2. Mini‑lecture (10 min): Introduce the piece‑wise definition of |f(x)|, illustrate with a linear example on the board.
3. Guided practice (15 min): Work through the quadratic example y = x² − 9, deriving the piece‑wise form and sketching both graphs.
4. Group activity (15 min): Using graphing software, explore a cubic (e.g., x³ − x) and a trig function (e.g., sin x). Identify reflected segments and corners; record observations.
5. Check for understanding (5 min): Quick exit‑ticket with two short questions – one conceptual, one sketch.
6. Summary (5 min): Recap the four key effects of the absolute‑value operation and link back to the success criteria.

Students summarise the transformation rules in their own words and hand in the exit ticket. For homework they will complete the worksheet, creating |f(x)| graphs for a linear, quadratic and sine function of their choice.