24-25 Alg1 3-7 FLASHCARD - 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 graph shifts vertically by c units. If c is positive, it shifts up; if negative, it shifts down.

The graph shifts horizontally to the right by c units. If c is negative, it shifts left.

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

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

The graph of the function is vertically stretched by a factor of 2.

The graph is reflected over the x-axis.

The graph shifts left by 3 units.

The graph shifts down by 4 units.