Linear Transformations (Trans. & Dilations)

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

It transforms the function to g(x) = -f(x), flipping the graph over the x-axis.

It transforms the function to g(x) = kf(x), where 0 < k < 1, making the graph closer to the x-axis.

The new function is g(x) = f(x) + c, where c is positive for an upward shift and negative for a downward shift.

It represents a horizontal compression or expansion of the function f(x) depending on the value of k.

The new function is g(x) = f(3x), which compresses the graph towards the y-axis.

It reflects the graph across the x-axis and shifts it down 3 units.

The new function is g(x) = f(x) - 4.

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

It indicates a horizontal compression by a factor of 3 and a vertical shift upward by 7 units.