Question

I need help with my math! Can you please help me!!

Answer 1

Answer:

$y=-|x-1|+3$

Step-by-step explanation:

The graph of the function ($y=|x|$) can be described as a perfect (v) shape composed of two lines with the equation ($y=x$) and ($y=-x$) with a range of ($y\geq 0$). In the depicted graph, this function has undergone some transfomrations. The general format for a transformation of an absolute value function is the following;

$y=(+-)n|x-k|+h$

The function can be inverted if the sign of (n) is (-). As per the given graph, the function is inverted, thus the answer will have a (-) sign in front of it. One can see that the (n) value has to be (1) or rather not present since the function has no scaling factor.

$y=-|x|$

The function has been shifted (k) units to the right, one can see that the given function's vertex is (1) unit to the right, thus the equation of the function has a (1) in the position of (k).

$y=-|x-1|$

The function is shifted (3) units up, thus the position of (h) is occupied by a (3).

$y=-|x-1|+3$

Therefore the following answer choice is correct, as it fits all of the requirements;

$y=-|x-1|+3$