Question

1. $x=|y+1|$

is this graph a function?

Explanation:

Step1: Recall function definition

A relation is a function if every input (x-value) has exactly one output (y-value). We use the Vertical Line Test: any vertical line drawn on the graph intersects the curve at most once.

Step2: Analyze the given graph/equation

For the equation $x=|y+1|$, rewrite it to solve for $y$:
When $y+1 \geq 0$ (i.e., $y \geq -1$), $x = y+1 \implies y = x - 1$.
When $y+1 < 0$ (i.e., $y < -1$), $x = -(y+1) \implies y = -x - 1$.
For a single positive $x$-value (e.g., $x=2$), we get two $y$-values: $y=2-1=1$ and $y=-2-1=-3$. This means a vertical line $x=2$ intersects the graph twice.

Answer:

No, this graph is not a function.