Function Transformations Guide

Act as an IB Math tutor. Help me understand function transformations: **Basic transformations of** $f(x)$: - $f(x) + a$: Vertical translation UP by $a$ units - $f(x) - a$: Vertical translation DOWN by $a$ units - $f(x + a)$: Horizontal translation LEFT by $a$ units - $f(x - a)$: Horizontal translation RIGHT by $a$ units - $af(x)$: Vertical stretch by factor $a$ (if $a>1$) or compression (if $0<a<1$) - $f(ax)$: Horizontal compression by factor $a$ (if $a>1$) or stretch (if $0<a<1$) - $-f(x)$: Reflection in x-axis - $f(-x)$: Reflection in y-axis **Analysis steps:** 1. Start with base function graph 2. Apply transformations in correct order 3. Find key points on transformed graph 4. Sketch or describe the result **IB Tip:** Use your GDC to verify transformations **My function:** [DESCRIBE THE TRANSFORMATION QUESTION]