On each coordinate plane, the parent function f of x is equal to absolute value of x is represented by a dashed line and a translation is represented by a solid line. Which graph represents the translation g of x is equal to start absolute value x plus 2 end absolute value as a solid line?
Answer
A
Image with description On a coordinate plane, a dashed line absolute value graph has a vertex at (0, 0). A solid line absolute value graph has a vertex at (2, 0).
B
Image with description On a coordinate plane, a dashed line absolute value graph has a vertex at (0, 0). A solid line absolute value graph has a vertex at (0, negative 2).
C
Image with description On a coordinate plane, a dashed line absolute value graph has a vertex at (0, 0). A solid line absolute value graph has a vertex at (negative 2, 0).
D
Image with description On a coordinate plane, a dashed line absolute value graph has a vertex at (0, 0). A solid line absolute value graph has a vertex at (0, 2).
Explanation
In g(x) = |x + 2|, adding 2 inside the absolute value shifts the parent graph y = |x| two units to the left. The vertex moves from (0, 0) to (−2, 0), which is shown in choice C.
AI-written and checked against the verified answer.