Linear Transformations (Translations)

Front

What is a linear transformation?

Back

A linear transformation is a function between two vector spaces that preserves the operations of vector addition and scalar multiplication.

Front

What is a translation in the context of linear transformations?

Back

A translation is a type of linear transformation that shifts a graph or function horizontally or vertically without changing its shape.

Front

If g(x) = f(x) + 4, what type of transformation is applied to f(x)?

Back

The transformation is a vertical translation upward by 4 units.

Front

If g(x) = f(x - 3), what type of transformation is applied to f(x)?

Back

The transformation is a horizontal translation to the right by 3 units.

Front

If g(x) = f(x + 2), what type of transformation is applied to f(x)?

Back

The transformation is a horizontal translation to the left by 2 units.

Front

If g(x) = f(x) - 5, what type of transformation is applied to f(x)?

Back

The transformation is a vertical translation downward by 5 units.

Front

What is the effect of adding a positive constant to a function's output?

Back

Adding a positive constant to a function's output results in a vertical shift upward.

Front

What is the effect of subtracting a positive constant from a function's output?

Back

Subtracting a positive constant from a function's output results in a vertical shift downward.

Front

What happens to the graph of f(x) when g(x) = f(x + 1)?

Back

The graph of f(x) shifts to the left by 1 unit.

Front

What happens to the graph of f(x) when g(x) = f(x - 1)?

Back

The graph of f(x) shifts to the right by 1 unit.