1. The problem asks us to analyze the function on the interval $[0,2[$ and determine whether it has absolute minimum and/or maximum values. 2. From the graph description, the function starts at $(0,2)$ and passes near $(1,1.5)$ and $(2,0)$, but the point at $(2,0)$ is an open circle, meaning the function is not defined at $x=2$. 3. Since the function is defined on $[0,2[$, it includes $x=0$ but excludes $x=2$. 4. At $x=0$, the function value is $2$, which is the highest point on the interval. 5. As $x$ approaches $2$ from the left, the function values approach $0$, but since the function is not defined at $2$, it does not attain the value $0$. 6. The function decreases continuously from $2$ at $x=0$ down to values approaching $0$ near $x=2$. 7. Therefore, the function has an absolute maximum value of $2$ at $x=0$. 8. However, it does not have an absolute minimum value on $[0,2[$ because it approaches $0$ but never attains it. 9. Hence, the correct answer is (c): the function has an absolute maximum value but not an absolute minimum value. Final answer: (c) has absolute maximum value but not absolute minimum value.