Question

adele and neil are discussing how to translate an absolute value function 2 units to the right and 4 units up. the absolute value function is $y = |x + 1| + 1$. adele says the answer is $y = |x + 3| + 5$. neil says the answer is $y = |x - 1| + 5$. who is correct? options: both, adele, neither, neil

Explanation:

Step1: Recall horizontal translation rule

For $y=|x-h|+k$, right shift by $a$: replace $x$ with $x-a$.

Step2: Apply right shift (2 units)

Original: $y=|x+1|+1 = |x-(-1)|+1$. Shift right 2: $y=|(x-2)+1|+1 = |x-1|+1$.

Step3: Apply vertical translation (4 units up)

Add 4 to the constant term: $y=|x-1|+1+4 = |x-1|+5$.

Step4: Match to Neil's answer

Neil's function matches the translated result.

Answer:

Neil