1. LEARNING GOALS FOR LESSON 2.6 Stretches/Compressions
Recognize sketch and write transformations of linear functions including (1) translation, (2) reflection, (3) stretch/compression
and (4) combination of transformations.
Translations
Horizontal
Vertical
Reflections
X-axis
Y-axis
Stretches/Compressions

2. Example 1: Translating & Reflecting Linear Functions
Let g(x) be the indicated transformation of f(x). Write the rule for g(x).
A. f(x) = x – 2 , horizontal translation 3 right
LG 2.6.1
f(x)
Rule:
g(x)
B. f(x) = 3x + 1; horizontal translation 2 units right
LG 2.6.1
f(x)
Rule:
g(x)
C. f(x) = 3x + 1; vertical translation 5 units up
LG 2.6.1
f(x)
Rule:
g(x)

3. Example 1B: Translating Reflecting Functions
LG 2.6.2
Write the rule for g(x). The following is a linear function defined in the table; Reflect across x-axis x –2 2
f(x) 1
Stretches and compressions change the _____ of a linear function.
If the line becomes. . .
STEEPER: stretched __________ or compressed ___________
FLATTER: compressed _________ or stretched _____________
These don’t change!
y–intercepts in a horizontal stretch or compression
x–intercepts in a vertical stretch or compression
Helpful Hint

4. Example 2: Stretching & Compressing Linear Functions
LG 2.6.3
Let g(x) be a horizontal compression of f(x) = –x + 4 by a factor of ½. Write the rule for g(x), and graph the function.
f(x)
Rule:
g(x)
Let g(x) be a vertical compression of f(x) = 3x + 2 by a factor of ¼. Write the rule for g(x) and graph the function.
f(x)
Rule:
g(x)

5. Ex 3: Combining Transformations of Linear Functions
LG 2.6.4
Let g(x) be a horizontal shift of f(x) = 3x left 6 units followed by a horizontal stretch by a factor of 4. Write the rule for g(x).
Step 1 First perform the translation.
Step 2 Then perform the stretch.
f(x)
Rule:
g(x)
h(x)
Let g(x) be a vertical compression of f(x) = x by a factor of ½ followed by a horizontal shift 8 left units. Write the rule for g(x).
f(x)
Rule:
g(x)
h(x)