Transformation involves changing the size and location of a function.
[tex]\mathbf{y = 2|x - 6|}[/tex] is produced by a vertical stretch, and a horizontal shift left.
An absolute function is represented as:
[tex]\mathbf{y = a|x - h| + k}[/tex]
The parameters are represented as:
[tex]\mathbf{(h,k) = (6,0)}[/tex] --- vertex
[tex]\mathbf{(x,y) = (8,4)}[/tex] --- point
Substitute [tex]\mathbf{(h,k) = (6,0)}[/tex] and [tex]\mathbf{(x,y) = (8,4)}[/tex] in [tex]\mathbf{y = a|x - h| + k}[/tex]
[tex]\mathbf{4 = a|8 - 6| + 0}[/tex]
[tex]\mathbf{4 = a|8 - 6|}[/tex]
[tex]\mathbf{4 = a|2|}[/tex]
Remove absolute brackets
[tex]\mathbf{4 = a \times 2}[/tex]
Divide both sides by 2
[tex]\mathbf{a= 2}[/tex]
Substitute [tex]\mathbf{a= 2}[/tex] and [tex]\mathbf{(h,k) = (6,0)}[/tex] in [tex]\mathbf{y = a|x - h| + k}[/tex]
[tex]\mathbf{y = 2|x - 6| + 0}[/tex]
[tex]\mathbf{y = 2|x - 6|}[/tex]
The parent function of an absolute function is:
[tex]\mathbf{y = |x|}[/tex]
A right translation is represented as:
[tex]\mathbf{y = |x - h|}[/tex]
And a vertical stretch is represented as:
[tex]\mathbf{y = a|x - h|}[/tex]
Hence,
[tex]\mathbf{y = 2|x - 6|}[/tex] is produced by option (d)
Read more about transformations at:
https://brainly.com/question/13801312
