Question

Write the equation of the absolute value function y = –|x| translated left 4 units.

Answer 1

Answer: y = -|x+4|

Explanation:

the formula for absolute value is

y = a|x-h| +k

(h, k), is your vertex

h, is your shift left or right

k, is your shift up or down

a, is your stretch and negative in front indicates a reflections.

if you want to shift he function left for that's -4 so substitut in your equations for h -4

y= -|x-(-4)|

y = -|x+4|

Answer 2

Explanation:

The equation of the absolute value function y = |x| is a V-shaped graph centered at the origin. To translate this graph left 4 units, we need to replace x with (x + 4) in the equation. Also, since the question asks for y = -|x|, we need to reflect the graph across the x-axis by multiplying the entire equation by -1. Therefore, the equation of the translated absolute value function is:

y = -|x + 4|

This equation represents a V-shaped graph that is centered at x = -4 and opens downward (since it is multiplied by -1), with the vertex at (-4,0).