Question

How do you graph `y =2 abs(x-4)+ 1`?

Answer 1

Graph the domain for `(x-4) <= 0` and then the domain for `(x-4)>= 0`

Explanation:

Note that the two components are both linear, so only 2 points are required for each.

For `(x-4) <=0`
`color(white)("XXXX")`if `x=4 rarr y = 2abs(0) + 1 = 1`
`color(white)("XXXX")`if `x = 0 rarr y = 2(abs-4) + 1 = 9`

For `(x-4) >= 0`
`color(white)("XXXX")`if `x=4 rarr y = 2abs(0) + 1 = 1`
`color(white)("XXXX")`if `x= 8 rarr y = 2abs(4)+1 = 9`