Short Answer 
The domain of the function is [0, ‚Äöau), indicating it is defined for x-values greater than or equal to zero. The range is (-‚Äöau, 4], meaning the function can produce y-values up to 4 while extending downwards indefinitely.
Step 1: Understanding Domain
The domain of a function refers to the set of all possible input values for which the function is defined. To determine the domain of a plotted function, examine the x-values on the graph. In this case, the function is only defined for values where x is greater than or equal to zero, which can be expressed as:
- Domain: [0, ‚Äöau)
Step 2: Understanding Range
The range of a function represents all possible output values that the function can produce. For the given function, we can see that the highest y-value it can reach is 4, while it can continue downward indefinitely. Therefore, the range of the function can be specified as:
- Range: (-‚Äöau, 4]
Step 3: Interpreting Numerical Intervals
Numerical intervals are a way to express the set of values within certain limits. For example, the interval [a, b] includes both endpoints a and b, while (a, b] includes b but not a. When using infinity, we denote intervals like [0, ‚Äöau) to indicate that one endpoint is included, while ‚Äöau itself is never included as it’s not a specific number. Thus, intervals help in specifying domains and ranges precisely.