# How do you graph  f(x) = 2abs x+1 ?

When $x \ge 0$ we have $f \left(x\right) = 2 \left\mid x \right\mid + 1 = 2 x + 1$, which is a straight line of slope $2$, starting from $\left(0 , 1\right)$
When $x \le 0$ we have $f \left(x\right) = 2 \left\mid x \right\mid + 1 = - 2 x + 1$, which is a straight line of slope $- 2$, ending at $\left(0 , 1\right)$
So $f \left(x\right)$ is basically a 'V' shape of slope $\pm 2$ with vertex at $\left(0 , 1\right)$