1. Section 1-5 Graphical Transformations

2. Section 1-5 vertical and horizontal translations vertical and horizontal translations reflections across the axes reflections across the axes vertical and horizontal stretches and shrinks vertical and horizontal stretches and shrinks combining transformations combining transformations

3. Vertical and Horizontal Translations horizontal translations horizontal translations y = f (x – c) shifts right by c units y = f (x – c) shifts right by c units examples: examples: y = f (x + c) shifts left by c units y = f (x + c) shifts left by c units examples: examples:

4. Vertical and Horizontal Translations vertical translations vertical translations y = f (x ) – c shifts down by c units y = f (x ) – c shifts down by c units examples: examples: y = f (x) + c shifts up by c units y = f (x) + c shifts up by c units examples: examples:

5. Reflections Across Axes reflection across the x-axis: y = – f (x) reflection across the x-axis: y = – f (x) examples: examples: reflection across the y-axis: y = f (– x) reflection across the y-axis: y = f (– x) examples: examples:

6. Vertical Stretches and Shrinks a vertical stretch makes the graph narrower a vertical stretch makes the graph narrower a vertical shrink makes the graph wider a vertical shrink makes the graph wider vertical stretch/shrink: vertical stretch/shrink: examples: examples:

7. Horizontal Stretches and Shrinks a horizontal stretch makes the graph wider a horizontal stretch makes the graph wider a horizontal shrink makes the graph narrower a horizontal shrink makes the graph narrower horizontal stretch/shrink: horizontal stretch/shrink: examples: examples:

8. Combining Transformations the order makes a difference the order makes a difference reflections are always applied first, but sometimes it is easier to sketch the graph by ignoring the reflection until the end reflections are always applied first, but sometimes it is easier to sketch the graph by ignoring the reflection until the end shift the graph into the correct position and then when you sketch it, make it narrower/wider and with any reflections shift the graph into the correct position and then when you sketch it, make it narrower/wider and with any reflections