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The answer is D. You move the problem Up three, right one, and you flip it.

If we start with the usual V shape of the parent function [tex] y=|x|[/tex], we can see that it was transformed as follows:

  • Shift 1 unit right: [tex] |x| \mapsto |x-1|[/tex] as a particular case of [tex] f(x)\mapsto f(x-1)[/tex]
  • Reflection across the x axis: [tex] |x-1|\mapsto -|x-1|[/tex] as a particular case of [tex] f(x)\mapsto -f(x)[/tex]
  • Shift 3 units up: [tex]-|x-1|\mapsto -|x-1|+3[/tex] as a particular case of [tex]f(x)\mapsto f(x)+3[/tex]

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