Horizontal Shift and Reflection Combined

Question:
Start with the parent function f of x equals x. First shift the graph 3 units to the right, then reflect it across the x-axis to create function h of x. Write the equation for h of x. Verify your equation by testing the point where the original function crosses the y-axis and where the transformed function crosses the y-axis.

Horizontal Shift and Reflection Combined

This lesson explores how to build a transformed linear function by applying a horizontal shift and an x-axis reflection to a parent function. Students write the equation of the resulting function and verify it by tracking key points through each transformation step.

In this lesson, you will learn to:
• Apply a horizontal shift to a linear parent function by replacing x with (x − c).
• Apply a reflection across the x-axis by multiplying a function by −1.
• Write the equation of a transformed linear function in slo