Graphs of Linear Transformations

The graph of g is a vertical translation 2 units up of the graph of f

The graph of f is a horizontal translation two units left of g

The graph of g is a vertical stretch by a factor of 2 of the graph of f

The graph of g is a reflection of the graph of f

The graph of g is a vertical translation 4 units up from the graph f

The graph of g is a horizontal translation of the graph of f, 4 units right

The graph of g is a horizontal translation of the graph of f, 4 units left

The graph of g is a vertical stretch of the graph of f, by a factor of 7

g(x)=|x+2|

g(x)=|x|+2

g(x)=|x-2|

g(x)=|x|-2

linear

constant

absolute value

quadratic

g(x) = f(x) - 5

g(x) = -f(x)

g(x) = f(x) + 5

g(x) = 3f(x)

g(x)= 1/3f(x)

$$g\left(x\right)=-f\left(x\right)$$

$$g\left(x\right)=\frac{1}{2}f\left(x\right)$$

$$g\left(x\right)=-f\left(x\right)+2$$

$$g\left(x\right)=2f\left(x\right)+4$$

Graph g is a reflection.

Graph g translated down 2 units.

Graph g is steeper.

Graph g is less steep.

Graph g rotated

Graph g translated down 4 units

Graph g translated up 4 units

Graph g reflected