Linear Transformation Retake 11/19

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

It shifts the graph of f(x) down by 5 units.

It shifts the graph of f(x) up by 2 units.

It makes the graph steeper and shifts it down by 5 units.

It makes the graph less steep (wider) by a factor of 4.

It shifts the graph of f(x) to the right by 3 units.

A vertical shift can be represented as f(x) + k, where k is the number of units to shift up (if k > 0) or down (if k < 0).

A horizontal shift can be represented as f(x - h), where h is the number of units to shift right (if h > 0) or left (if h < 0).

Multiplying a function by a constant greater than 1 makes the graph steeper, while multiplying by a constant between 0 and 1 makes it less steep.

A negative constant reflects the graph across the x-axis.