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 effect of multiplying a function by a factor less than 1?

Back

It compresses the graph vertically, making it less steep.

Front

What happens when a function is shifted down by a constant?

Back

The entire graph of the function moves down by that constant value.

Front

What is the parent function for linear transformations?

Back

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

Front

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

Back

It represents a vertical shift of the graph of f(x) by c units.

Front

What does the transformation g(x) = af(x) do if a > 1?

Back

It stretches the graph vertically by a factor of a.

Front

What does the transformation g(x) = af(x) do if 0 < a < 1?

Back

It compresses the graph vertically by a factor of a.

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) = f(x) + 3, what is the transformation?

Back

The graph of f(x) is shifted up 3 units.

Front

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

Back

It represents a horizontal shift of the graph of f(x) to the right by c units.