1. **Problem Statement:** We are given a function defined on the interval $[0,2[$ and asked to determine whether it has an absolute minimum and/or maximum value on this interval. 2. **Understanding the Interval:** The interval $[0,2[$ means $x$ ranges from 0 inclusive to 2 exclusive. So the function is defined at $x=0$ but not at $x=2$. 3. **Observing the Graph:** - At $x=0$, the function value is $f(0) = 2$. - At $x=1$, the function value is $f(1) = 0$. - As $x$ approaches 2 from the left, the function value decreases steeply toward $-2$ but the function is not defined at $x=2$. 4. **Absolute Maximum:** The highest value on the interval is at $x=0$ with $f(0) = 2$. Since $0$ is included in the domain, the function attains its absolute maximum value of 2. 5. **Absolute Minimum:** The function values decrease toward $-2$ as $x$ approaches 2, but since $x=2$ is not included, the function never actually attains $-2$. It gets arbitrarily close but does not reach it. Therefore, there is no absolute minimum value on $[0,2[$. 6. **Conclusion:** The function has an absolute maximum value but no absolute minimum value on the interval $[0,2[$. **Final answer:** (c) has absolute maximum value but not absolute minimum value