Question

Which function is a translation of the parent absolute value function?
f(x) = mc014-1.jpg
f(x) = mc014-2.jpg
f(x) = mc014-3.jpg
f(x) = mc014-4.jpg

Answer 1

I can't see the image files you listed. Could you either paste the four function expressions here or upload the images?

Meanwhile, a quick rule to identify the translation(s) of the parent absolute-value y = |x|:
- A pure translation (no reflection or dilation) has the form f(x) = |x − h| + k (or |x + h| + k) where the coefficient of the absolute value is +1.
- If there's a factor a in front so f(x) = a|x − h| + k with a ≠ 1, that's a vertical dilation (not a pure translation).
- If a < 0, there's a reflection across the x-axis as well.

If you paste the four expressions I’ll pick which one(s) are translations.