12-3-24 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 is the parent function of linear equations?

Back

The parent function of linear equations is represented by the equation y = x.

Front

What happens to the graph of f(x) = x when it is multiplied by a factor less than 1?

Back

The graph becomes less steep, indicating a vertical compression.

Front

If f(x) = x is transformed to g(x) = ⅓f(x), how does the steepness change?

Back

The graph of f is steeper than the graph of g.

Front

What does a vertical translation of a graph mean?

Back

A vertical translation shifts the graph up or down without changing its shape.

Front

What is the effect of shifting the graph of f(x) = x down by 7 units?

Back

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

Front

How does the graph of f(x) = x change when it is reflected over the x-axis?

Back

The new graph will be represented by g(x) = -f(x) or g(x) = -x.

Front

What is the result of applying a vertical stretch by a factor of 2 to f(x) = x?

Back

The new function is g(x) = 2f(x) or g(x) = 2x.

Front

What does it mean for a graph to be less steep by a factor of 1/4?

Back

It means the slope of the graph is reduced, making it flatter compared to the original graph.

Front

What is the transformation when f(x) = x is replaced with g(x) = 2f(x)?

Back

The graph is vertically stretched by a factor of 2.