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

If the graph of f(x) = x is shifted down 2 units, what is the new equation?

Back

f(x) = x - 2.

Front

What does it mean to shift a graph up or down?

Back

Shifting a graph up or down means adding or subtracting a constant from the function's output.

Front

How does multiplying a function by a constant affect its steepness?

Back

Multiplying a function by a constant greater than 1 makes the graph steeper, while a constant between 0 and 1 makes it less steep.

Front

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

Back

A negative coefficient reflects the graph across the x-axis.

Front

What transformation occurs when f(x) = x is changed to g(x) = x + 4?

Back

The graph is shifted up 4 units.

Front

What is the equation of a function that is three times as steep as f(x) = x?

Back

g(x) = 3x.

Front

If g(x) = -x, what transformation has occurred compared to f(x) = x?

Back

The graph has been reflected across the x-axis.

Front

What does it mean for a graph to be 'shifted'?

Back

A graph is 'shifted' when it is moved vertically or horizontally without changing its shape.