Review: Linear Transformations

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

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

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

The transformation g(x) = f(x) - 3 translates the graph of f(x) down by 3 units.

A negative slope indicates that as x increases, y decreases, resulting in a downward slant of the graph.

The transformation g(x) = 4f(x) makes the graph steeper by a factor of 4.

The transformation g(x) = (1/4)f(x) compresses the graph vertically by a factor of 1/4.

Reflection in linear transformations refers to flipping the graph over a specific axis, such as the x-axis or y-axis.

The y-intercept is the point where the graph crosses the y-axis, representing the value of the function when x = 0.

A function is considered 'steeper' if it has a larger absolute value of the slope, indicating a greater change in y for a given change in x.