Question

question 13 (1 point)
compare the equation to the absolute value parent function ($y = |x|$). select all the transformations that apply.
$y = -|x|$

a reflected over the x - axis
b horizontal shift left
c horizontal shift right
d vertical shift up
e vertical shift down
f graph is narrower
g graph is wider

Explanation:

To determine the transformations of \( y = -|x| \) from the parent function \( y = |x| \):

• A negative sign in front of the absolute - value function reflects the graph over the \( x \) - axis. For a function \( y = f(x) \), the function \( y=-f(x) \) is a reflection of \( y = f(x) \) over the \( x \) - axis. Here, \( f(x)=|x| \), so \( y=-|x| \) is a reflection of \( y = |x| \) over the \( x \) - axis.
• There is no horizontal shift because the form is \( y=-|x - h|+k \) with \( h = 0 \), so no left or right shift.
• There is no vertical shift because \( k = 0 \) in the form \( y=-|x - h|+k \), so no up or down shift.
• The coefficient of the absolute - value term is \( - 1 \) (the absolute value of the coefficient is \( 1 \), same as the parent function), so the graph is not narrower or wider.

Answer:

a. Reflected over the x - axis