Question

Which equation is represented by the graph?

A) Y=-|x-3|+1
B) y=|x+1|+3
C)-|x+3|+1
D)-|x-1|+3

Answer 1

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

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

Answer 2

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