Linear Transformation with Key Attributes

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 effect of adding a constant to a function f(x)?

Back

Adding a constant to a function f(x) results in a vertical translation of the graph of the function.

Front

What happens to the graph of f(x) when f(x) is replaced with f(x) + 2?

Back

The graph of f(x) is translated vertically upwards by 2 units.

Front

What is a horizontal translation in the context of function graphs?

Back

A horizontal translation shifts the graph of a function left or right along the x-axis.

Front

If g(x) = f(x - 4), what transformation occurs?

Back

The graph of g is a horizontal translation of the graph of f, 4 units to the right.

Front

If g(x) = f(x + 4), what transformation occurs?

Back

The graph of g is a horizontal translation of the graph of f, 4 units to the left.

Front

What is a vertical stretch in relation to a function?

Back

A vertical stretch occurs when the output of a function is multiplied by a factor greater than 1, making the graph taller.

Front

What is a vertical compression in relation to a function?

Back

A vertical compression occurs when the output of a function is multiplied by a factor between 0 and 1, making the graph shorter.

Front

What does it mean to reflect a graph across the x-axis?

Back

Reflecting a graph across the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

Front

What is the transformation of f(x) when it is replaced with -f(x)?

Back

The graph of f(x) is reflected across the x-axis.