Transformations of Linear Functions

Front

What is the linear parent function?

Back

y = x

Front

What happens when f(x) = x is replaced with 2f(x)?

Back

Vertical stretch by a factor of 2

Front

What transformation occurs when f(x) = x is replaced with f(x) + 2?

Back

Vertical translation up by 2 units.

Front

How does the equation y = f(x) + c shift the graph?

Back

Shifted up 'c' units

Front

What transformation occurs when f(x) = x is transformed to g(x) = f(x + 3)?

Back

g(x) is shifted left 3 units

Front

What is a vertical translation?

Back

A shift of the graph up or down without changing its shape.

Front

What is a horizontal translation?

Back

A shift of the graph left or right without changing its shape.

Front

What does a vertical stretch do to a graph?

Back

It makes the graph taller by multiplying the function by a factor greater than 1.

Front

What does a vertical compression do to a graph?

Back

It makes the graph shorter by multiplying the function by a factor between 0 and 1.

Front

What is the effect of replacing f(x) with f(x - c)?

Back

The graph shifts to the right by 'c' units.