ALGEBRA 2 LECTURE F – 3: Transformations
Reading Assignment: Chapter 2, Pages 133 – 141
TRANSLATIONS

If y = f(x), then y = f(x) + k gives a vertical translation of the graph of f.
o The translation is k units up for k > 0 and k units down for k < 0.

If y = f(x), then y = f(x – h) gives a horizontal translation of the graph of f.
o The translation is h units to the right for h >0 and h units to the left for h < 0.

Page 139 #6: Identify the transformations from f to g: f(x) = x2 and g(x) = x2 – 3
TRY THIS Page 134: Identify the transformation from f to g:
A. f(x) = x2 and g(x) = x2 – 2
B. f(x) = x and g(x) = x – 3
ALGEBRA 2 LECTURE F – 3: Transformations
VERTICAL STRETCH AND COMPRESSION

If y = f(x), then y = a f(x) gives a vertical stretch or compression of the graph of f.
o If a > 1, the graph is stretched vertically by a factor of a.
o If 0 < a < 1, the graph is compressed vertically by a factor of a.

A vertical stretch or compression moves the graph away from or toward the x-axis
respectively.
HORIZONTAL STRETCH AND COMPRESSION

If y = f(x), then y = f(b x) gives a horizontal stretch or compression of the graph of f.
o If b > 1, the graph is compressed horizontally by a factor of 1/b.
o If 0 < b < 1, the graph is stretched horizontally by a factor of 1/b.

A horizontal stretch or compression moves the graph away from or toward the y-axis
respectively.
ALGEBRA 2 LECTURE F – 3: Transformations
4
Page 139 #7: Identify the transformations from f to g, f(x) = √9 − 𝑥 2 and g(x) = √9 − 𝑥 2
3
Page 139 #8: Identify the transformation from f to g, f(x) = √36 − 𝑥 2 and g(x) = √36 − (2𝑥)2
TRY THIS Page 135:
Identify the transformation from f to g.
A. f(x) = √25 − 𝑥 2 and g(x) = 3√25 − 𝑥 2
1
B. f(x) = √25 − 𝑥 2 and g(x) = 3 √25 − 𝑥 2
TRY THIS Page 136: Identify the transformation from f to g.
A. f(x) = √25 − 𝑥 2 and g(x) = √25 − (3𝑥)2
1
B. f(x) = √25 − 𝑥 2 and g(x) = √25 − (4 𝑥)2
REFLECTIONS

If y = f(x), then y = – f(x) gives a reflection of the graph of f across the x – axis.
ALGEBRA 2 LECTURE F – 3: Transformations

If y = f(x), then y = f(– x) gives a reflection of the graph of f across the y – axis.
 Page 139 #9: Identify the transformation from f to g:
f(x) = – 3x + 1 and g(x) = – 3(– x) + 1
TRY THIS Page 137: Identify the transformation from f to g:
A. f(x) = x and g(x) = –x
B. f(x) = 2x – 1 and g(x) = 2(– x) – 1
SUMMARY OF TRANSFORMATIONS
HW F – 3 :
Pages 139 – 140 #11, 13, 17, 19, 25, 27, 31, 33, 35, 39, 43, 45, 47, 49, 63