Question

which of the following graphs represents y as a function of x where y is the distance from -2? a. b. c. d.

Explanation:

Step1: Recall distance formula

The distance $y$ from a number $x$ to - 2 is given by $y = |x - (-2)|=|x + 2|$.

Step2: Analyze the vertex of the absolute - value function

The vertex of the absolute - value function $y = |x + 2|$ occurs when $x+2 = 0$, i.e., $x=-2$. When $x=-2$, $y = 0$.

Step3: Check each graph

Graph A has its vertex at $x = 2$. Graph B has its vertex at $x = 0$. Graph C has its vertex at $x=-2$. Graph D has its vertex at $x = 2$.

Answer:

C.