Video: Finding the Domain of a Piecewise Defined Function given Its Graph

Determine the domain of the function represented by the given graph.

01:24

Video Transcript

Determine the domain of the function represented by the given graph.

The domain of a function is the complete set of possible values of the independent variable. In other words, it’s the set of all 𝑥-values which make the function work and will output real 𝑦-values. First thing we should take note of is that each of these lines have arrows, which means they extend forever.

So now we need to check which 𝑥-values will make this function work, whether there’s actually 𝑦-values that we can land on. So let’s start at zero for 𝑥. At zero for 𝑥, we land on around four and a half for 𝑦. So there is somewhere it will work.

As we go to the right, there’s lots of places that will work. And since our function actually extends out to the right, the blue line, every value to the right, all of these integers and actually all of the decimals in between these integers, will work as well.

As we go into the negatives, we can land on any 𝑥-value except that negative four. There are two open circles, which means you can’t actually land there. It won’t work at negative four. So our domain would be all the real numbers except for negative four, so all reals minus negative four.

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