Graphical Transformations

1
Section 1-5

• Graphical Transformations

2
Section 1-5

• vertical and horizontal translations
• reflections across the axes
• vertical and horizontal stretches and shrinks
• combining transformations

3
Vertical and Horizontal Translations

• horizontal translations
• y f (x c) shifts right by c units
• examples
• y f (x c) shifts left by c units
• examples

4
Vertical and Horizontal Translations

• vertical translations
• y f (x ) c shifts down by c units
• examples
• y f (x) c shifts up by c units
• examples

5
Reflections Across Axes

• reflection across the x-axis y f (x)
• examples
• reflection across the y-axis y f ( x)
• examples

6
Vertical Stretches and Shrinks

• a vertical stretch makes the graph narrower
• a vertical shrink makes the graph wider
• vertical stretch/shrink
• examples

7
Horizontal Stretches and Shrinks

• a horizontal stretch makes the graph wider
• a horizontal shrink makes the graph narrower
• horizontal stretch/shrink
• examples

8
Combining Transformations

• 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
• shift the graph into the correct position and
  then when you sketch it, make it narrower/wider
  and with any reflections