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 does it mean for a graph to be 'steeper'?

Back

A graph is considered 'steeper' when the slope of the line is greater, indicating a larger change in y for a given change in x.

Front

What is the effect of a vertical stretch on a graph?

Back

A vertical stretch multiplies the y-values of a function by a factor greater than 1, making the graph taller.

Front

What does a reflection over the x-axis do to a graph?

Back

A reflection over the x-axis flips the graph vertically, changing the sign of all y-values.

Front

How does shifting a graph up affect its equation?

Back

Shifting a graph up by k units adds k to the y-values, resulting in the equation f(x) + k.

Front

What is the parent function of linear equations?

Back

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

Front

What does a horizontal shift to the right mean for a function's equation?

Back

A horizontal shift to the right by h units changes the function to f(x - h).

Front

What is the impact of a negative coefficient in front of a function?

Back

A negative coefficient reflects the graph over the x-axis.

Front

What does it mean for a graph to be 'flatter'?

Back

A graph is 'flatter' when the slope is less than 1, indicating a smaller change in y for a given change in x.

Front

How do you describe a transformation that combines reflection and vertical stretch?

Back

This transformation reflects the graph over the x-axis and then stretches it vertically by a factor greater than 1.