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 effect does multiplying a function by a factor greater than 1 have on its graph?

Back

It results in a vertical stretch of the graph.

Front

What effect does multiplying a function by a factor between 0 and 1 have on its graph?

Back

It results in a vertical compression of the graph.

Front

What is the parent function for linear transformations?

Back

The parent function for linear transformations is f(x) = x.

Front

What does it mean to shift a graph vertically?

Back

Shifting a graph vertically means moving it up or down without changing its shape.

Front

What does it mean to shift a graph horizontally?

Back

Shifting a graph horizontally means moving it left or right without changing its shape.

Front

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

Back

It reflects the graph across the x-axis.

Front

If f(x) = x is transformed to g(x) = x + 3, what type of transformation occurs?

Back

A vertical shift up by 3 units.

Front

If f(x) = x is transformed to g(x) = x - 5, what type of transformation occurs?

Back

A vertical shift down by 5 units.

Front

If f(x) = x is transformed to g(x) = 2x, what type of transformation occurs?

Back

A vertical stretch by a factor of 2.