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 slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the ratio of the vertical change to the horizontal change between two points on the line.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-coordinate increases, the y-coordinate also increases, resulting in an upward trend.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-coordinate increases, the y-coordinate decreases, resulting in a downward trend.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating no vertical change as the x-coordinate changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because it does not have a horizontal change.

Front

How does the slope affect the steepness of a line?

Back

A larger absolute value of the slope indicates a steeper line, while a smaller absolute value indicates a less steep line.

Front

What transformation occurs when a graph is shifted up?

Back

When a graph is shifted up, all points on the graph move vertically in the positive y-direction.

Front

What transformation occurs when a graph is shifted down?

Back

When a graph is shifted down, all points on the graph move vertically in the negative y-direction.

Front

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

Back

A reflection over the x-axis means that for every point (x, y) on the graph, the corresponding point on the reflected graph is (x, -y).