1. The problem asks to estimate the value of the function $g$ at $x=0.9$ using the graph. 2. From the graph description, the function $g$ is piecewise linear with segments: - From $(-2,1)$ to $(0,1)$ - From $(0,0)$ to $(1,0)$ - From $(1,-1)$ to $(2,-1)$ 3. Since $0.9$ lies between $0$ and $1$, we focus on the segment from $(0,0)$ to $(1,0)$. 4. This segment is a horizontal line at $y=0$, so for any $x$ in $[0,1]$, $g(x) = 0$. 5. Therefore, $g(0.9) = 0$. 6. The function is defined at $x=0.9$ and the value is $0$. Final answer: $g(0.9) = 0$