Translation (Algebraic Transformations)
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Definition
In Algebra 1, a translation refers to a transformation of a graph where the entire graph is moved from one location to another without changing its shape, size, or orientation. A translation shifts every point of the graph the same distance in the same direction.
Key Points of Translation:
Horizontal Translation: A shift left or right along the x-axis.
Vertical Translation: A shift up or down along the y-axis.
General Definition:
A translation is a movement of a function or graph by adding or subtracting constants to its input (for horizontal shifts) or output (for vertical shifts).
Horizontal Translation:
If you transform f(x) to f(x + h), the graph shifts left by h units if h > 0, and right by h units if h<0.
Vertical Translation:
If you transform f(x) to f(x) + k, the graph shifts up by k units if k > 0, and down by k units if k < 0.
Example:
For f(x) = x^2, a translation of f(x) + 3 moves the graph 3 units up.
For f(x) = x^2, a translation of f(x - 2) moves the graph right by 2 units.
Why Does This Happen?
Horizontal translations: Adjusting x by adding or subtracting a constant changes the input for each point, shifting the entire graph left or right.
Vertical translations: Adding or subtracting a constant to f(x) changes the output for each point, shifting the graph up or down.
Summary:
A translation in algebra is a transformation that shifts the graph of a function horizontally (left or right) or vertically (up or down), without changing the shape of the graph.