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 linear parent function?

Back

The linear parent function is y = x, which represents a straight line through the origin with a slope of 1.

Front

What happens to the graph of f(x) when it is replaced with 2f(x)?

Back

The graph undergoes a vertical stretch by a factor of 2.

Front

What is the effect of adding a constant to a function, such as f(x) + 2?

Back

It results in a vertical translation of the graph up by 2 units.

Front

What does it mean for a graph to be reflected across the x-axis?

Back

It means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

Front

How does a vertical compression by a factor of 1/2 affect the graph of a function?

Back

It makes the graph flatter, reducing the distance of points from the x-axis.

Front

What is the effect of a horizontal compression by a factor of 1/2 on the graph of a function?

Back

It makes the graph narrower, pulling points closer to the y-axis.

Front

What transformation occurs when f(x) is replaced with f(x - 3)?

Back

The graph shifts to the right by 3 units.

Front

What transformation occurs when f(x) is replaced with f(-x)?

Back

The graph is reflected across the y-axis.

Front

What does the term 'steeper' refer to in the context of graph transformations?

Back

A steeper graph has a greater slope, indicating that it rises or falls more sharply.