Algebra-2

Horizontal Translations
A horizontal translation shifts the graph left or right.
The general form for horizontal translation is y = f(x − h), where:
If h > 0, the graph shifts right by h units.
If h < 0, the graph shifts left by ∣h∣ units.

Example:
y = f(x − 3) shifts the graph of f(x) 3 units to the right.
y = f(x + 3) shifts the graph of f(x) 3 units to the left.

Vertical Translations
A vertical translation shifts the graph up or down.
The general form for vertical translation is y = f(x) + k, where:
If k > 0, the graph shifts up by k units.
If k < 0, the graph shifts down by ∣k∣ units.

Example:
y = f(x) + 5 shifts the graph 5 units up.
y = f(x) − 2 shifts the...