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Home / 01 Mathematical Functions / 08 Domain and Range Visually

Determine the domain and range of the function shown below.


Solution

We can determine the domain and range by direct inspection of the graph. Remember to read the domain from left to right. Since we are moving horizontally, that means we read the \(x\) values, leftmost to rightmost. For the range, do the same from bottom to top. Similarly, this means are are looking for the bottommost \(y\) value to the topmost. The range tends to throw some students off, so make sure to really look closely and go from bottom to top. Because this graph is interactive, you should be able to select the minimal point on the right to determine the correct \(y\) value for the range.

Domain: \(\left[-1,1.75\right]\)
Range: \(\left[1.122,3.5\right]\)