# How do you graph y = 2 | x - 1 | - 3?

Mar 18, 2018

See below

#### Explanation:

Consider the standard graph of $f \left(x\right) = \left\mid x \right\mid$ below.

graph{absx [-10, 10, -5, 5]}

Then the graph of $y = 2 \left\mid x - 1 \right\mid - 3$ is this graph after the following transformations

Shift 1 unit positive in $x$ ("Right")
Scale by 2 units
Shift 3 units negative in $y$ ("Down")

Shown below:

graph{2abs(x-1)-3 [-10, 10, -5, 5]}