Question

question 15 (1 point)
compare the equation to the absolute value parent function ($y = |x|$). select all the transformations that apply.
$y = 2|x + 4|$

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:

Step1: Analyze Vertical Stretch/Compression and Reflection

For the absolute value function \( y = a|x - h|+k \), the coefficient \( a \) affects vertical stretch/compression and reflection. Here, \( a = 2 \) (positive, so no reflection over x - axis) and \( |a|=2>1 \), so the graph is vertically stretched (narrower).

Step2: Analyze Horizontal Shift

The term \( (x + 4) \) can be written as \( (x-(-4)) \). In the form \( y = |x - h| \), \( h=-4 \). A horizontal shift is \( h \) units. If \( h<0 \), it is a shift to the left by \( |h| \) units. So \( x+4 \) means a horizontal shift left by 4 units.

Step3: Analyze Vertical Shift

The equation \( y = 2|x + 4| \) has \( k = 0 \), so there is no vertical shift (neither up nor down).

Answer:

b. Horizontal Shift Left
f. Graph is Narrower