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 for linear transformations?

Back

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

Front

What does a vertical translation of a function involve?

Back

A vertical translation involves shifting the graph of the function up or down along the y-axis.

Front

If f(x) = -3x + 6 is transformed vertically up 9 units, what is g(x)?

Back

g(x) = -3x + 15.

Front

What does a reflection across the x-axis do to a function?

Back

A reflection across the x-axis inverts the output values of the function, changing f(x) to -f(x).

Front

What does the transformation g(x) = f(x) - 6 represent?

Back

g(x) is shifted down 6 units.

Front

What does the transformation g(x) = f(x - 6) represent?

Back

g(x) is shifted right 6 units.

Front

What is the effect of multiplying a function by a negative scalar?

Back

Multiplying a function by a negative scalar reflects the graph across the x-axis.

Front

What does the transformation g(x) = f(x) + 3 represent?

Back

g(x) is shifted up 3 units.

Front

How does a horizontal translation differ from a vertical translation?

Back

A horizontal translation shifts the graph left or right, while a vertical translation shifts it up or down.