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 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

How does shifting a graph down affect its equation?

Back

Shifting a graph down by 'k' units results in subtracting 'k' from the function's output, changing f(x) to f(x) - k.

Front

What is the effect of the transformation g(x) = -f(x)?

Back

The transformation g(x) = -f(x) reflects the graph of f across the x-axis.

Front

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

Back

The graph of f has been shifted down 4 units.

Front

What is the parent function of linear transformations?

Back

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

Front

What does the transformation g(x) = f(x) - 6 represent?

Back

The transformation g(x) = f(x) - 6 represents a vertical shift of the graph down by 6 units.

Front

If the graph of f(x) = x is shifted down 7 units, what is the new equation?

Back

The new equation is f(x) = x - 7.

Front

What is the general form of a linear transformation?

Back

The general form of a linear transformation can be expressed as T(x) = Ax + b, where A is a matrix and b is a vector.

Front

What is the significance of the slope in a linear function?

Back

The slope indicates the rate of change of the function; it represents how much y changes for a unit change in x.