Linear Transformations - Translations

Front

What is a linear transformation?

Back

A linear transformation is a function that maps a vector space to another vector space, preserving 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 happens to the graph of f(x) = x when it is transformed to g(x) = f(x) - 6?

Back

The graph is shifted down 6 units.

Front

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

Back

The graph is shifted right 3 units.

Front

Is the transformation g(x) = f(x + 6) a horizontal or vertical translation?

Back

It is a horizontal translation.

Front

What is the effect of the transformation g(x) = f(x) - 3 on the graph of f(x) = x?

Back

The graph is shifted down 3 units.

Front

What does the transformation g(x) = f(x) + 6 do to the graph of f(x) = x?

Back

The graph is shifted up 6 units.

Front

How does the transformation g(x) = f(x + 2) affect the graph?

Back

The graph is shifted left 2 units.

Front

What is the difference between vertical and horizontal translations?

Back

Vertical translations shift the graph up or down, while horizontal translations shift the graph left or right.

Front

If g(x) = f(x) + k, what does k represent?

Back

k represents a vertical shift; if k is positive, the graph shifts up, and if k is negative, it shifts down.