How do you graph f(x)=2|x-1|-3?

1 Answer
Oct 3, 2016

Use the graph of the parent function f(x)=absx but change the slope to of each half of the graph to +-2, and shift the vertex right one unit and down three units.

Explanation:

The parent function of absolute value is f(x)=abs(x) and looks like
the graph below. Note the vertex is at (0,0) and the slope of the left branch of the graph is -1 while the slope of the right branch is +1.
graph{abs(x) [-10, 10, -5, 5]}

Given the form, f(x)=mabs(x-h)+k,

+-m represents the slope of each branch of the graph. A positive value of m in the original equation means the graph has a "V" shape, while a negative value of m means the graph has an "upside-down V-shape".

(h,k) is the vertex. The vertex is shifted horizontally by h units and vertically by k units.

f(x)=2abs(x-1)-3

In this example, m=2 is positive, and the graph will have a V-shape. The left branch of the V has a slope of -2 and the right branch has a slope of 2.

The vertex is (1,-3), which represents a shift of one unit to the right and 3 units down.
graph{2abs(x-1)-3 [-10, 10, -5, 5]}