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 of linear transformations?

Back

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

Front

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

Back

It makes the graph steeper.

Front

What does adding a constant to a function do to its graph?

Back

It shifts the graph vertically. Adding a positive constant shifts it up, while adding a negative constant shifts it down.

Front

What is the transformation of g(x) = 3f(x) + 5 from f(x) = x?

Back

The graph is steeper and shifted up 5 units.

Front

What is the transformation of g(x) = f(x) - 6 from f(x) = x?

Back

The graph is shifted down 6 units.

Front

What is the transformation of g(x) = f(x) + 3 from f(x) = x?

Back

The graph is shifted up 3 units.

Front

What does a vertical stretch by a factor of k do to the graph of a function?

Back

It multiplies the y-values of the function by k, making the graph taller.

Front

What does a horizontal translation of a graph involve?

Back

It involves shifting the graph left or right along the x-axis.

Front

What is the effect of a negative sign in front of a function, such as g(x) = -f(x)?

Back

It reflects the graph across the x-axis.