Linear Transformations

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 the parent function of linear functions?

Back

The parent function of linear functions is f(x) = x.

Front

What happens to the graph of f(x) = x when it is transformed to g(x) = f(x - 3)?

Back

The graph is shifted right 3 units.

Front

What happens to the graph of f(x) = x when it is transformed to g(x) = f(x + 3)?

Back

The graph is shifted left 3 units.

Front

What does the transformation g(x) = f(-x) represent?

Back

It represents a reflection over the y-axis.

Front

If the function g(x) is translated 3 units up from f(x), what is the new equation?

Back

g(x) = f(x) + 3.

Front

What does the transformation g(x) = f(x + 6) indicate?

Back

The graph is shifted left 6 units.

Front

What is the effect of adding a positive number to the function f(x)?

Back

It shifts the graph upward.

Front

What is the effect of subtracting a positive number from the function f(x)?

Back

It shifts the graph downward.

Front

What does the transformation g(x) = f(-x + 2) indicate?

Back

It reflects the graph over the y-axis and shifts it right 2 units.