1. PreCalculus Chapter 1 Section 6
Graphical Transformations

2. Transformations
In this section we will look at both rigid transformations and non- rigid transformations.
Rigid Transformations: leave the size and shape of the graph unchanged. These include translations, reflections, or any combination of these.
Non-rigid Transformations: distort the shape of the graph. These include horizontal & vertical stretches and shrinks.

3. Translations
Let c be a positive real number. Then the following transformations result in translations of the graph.
Horizontal Translations
y = f(x – c) a translation to the right by c units.
y = f(x + c) a translation to the left by c units.
Vertical Translations
y = f(x) + c a translation up by c units
y = f(x) – c a translation down by c units

4. Reflections Across the x-axis: y = - f(x) Across the y-axis: y = f(-x)
See diagram on page 141

5. Graphing Absolute Value Compositions
Given the graph of y = f(x),
The graph of y = ∣f(x)∣ can be obtained by making all y-values positive and reflecting the portion of the graph below the x-axis to the top-side of the x-axis.
The graph of y = f(∣x∣) can be obtained by all x-values positive and reflecting the portion of the graph left of the y-axis to the right-side of the y-axis.
See exploration #2 on page 143.

6. Vertical & Horizontal Stretches and Shrinks
Let c be a positive real number.
Horizontal Stretches & Shrinks:
y = f (c x) a stretch by a factor 1/c if c < 1
a shrink by a factor of 1/c if c > 1
Vertical Stretches & Shrinks:
y = c f(x) a stretch by a factor of c if c > 1
a shrink by a factor of c if c < 1
See exploration # 3 on page 144.

7. Homework
# 3 – 54 by multiples of 3 on pages 147 – 148.