Question

The graph of y=|x| is transformed as shown in the graph below. Which equation represents the transformed function?

Answer 1

we have that

the original function $y=\left|x\right|$ has the vertex at point $(0,0)$

The transformed function has the vertex at point $(-3,-2)$

so

the rule of the translation is equal to

$(x,y)------> (x-3,y-2)$

That means

The translation is $3$ units to the left and $2$ units down

therefore

the answer is

the transformed function is $y=\left|x+3\right|-2$

Answer 2

The vertex of the graph y=|x| is at (0,0)

After transformation the vertex becomes at (-3,-2)
Apply axes transformation from (0,0) to (h,k)
So, the transformation rule is (x,y) → (x-h, y-k)
(h,k) will be equal (-3,-2)


∴ y=|x| ⇒ (y-(-2)) = |x-(-3)|
∴(y+2) = |x+3|
∴ y = |x+3|-2


So, the correct answer is option 2