Multiple Transformations and Function Composition

Question:
The linear function p of x equals negative 3x plus 2 undergoes the following transformations in order: first, shift left 4 units; second, stretch vertically by a factor of 2; third, shift down 6 units. Write the equation of the final transformed function q of x. Find three points on the original function and verify where they map to on the transformed function.

Multiple Transformations and Function Composition

This lesson applies three sequential transformations — a horizontal shift left, a vertical stretch, and a vertical shift down — to a linear function. Students derive the equation of the final function step by step and verify the result by tracing three specific points through each transformation.

In this lesson, you will learn to:
• Apply horizontal and vertical shifts and vertical stretches to a linear function one step at a time
• Derive a single combined transformat