Question

question 11 (1 point)
compare the equation to the absolute value parent function ($y = |x|$). select all the transformations that apply.
$y = |x + 2|$

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: Recall Transformations

For absolute value functions \( y = |x - h| + k \), horizontal shift is determined by \( h \), vertical by \( k \), reflection by sign, and width by coefficient. Here, \( y = |x + 2| = |x - (-2)| \), so \( h=-2 \), \( k = 0 \), coefficient is \( 1 \).

Step2: Analyze Each Option

• a: No negative sign outside, so no reflection over x - axis.
• b: \( h=-2 \), so horizontal shift left (since \( h < 0 \), shift left \( |h| \) units).
• c: Opposite of b, incorrect.
• d: \( k = 0 \), no vertical shift up.
• e: \( k = 0 \), no vertical shift down.
• f: Coefficient is 1, same width as parent, not narrower.
• g: Coefficient is 1, same width as parent, not wider.

Answer:

b. Horizontal Shift Left