Question Video: Determining the Range of a Piecewise-Defined Function from Its Graph Mathematics

Find the range of the function.

01:20

Video Transcript

Find the range of the function.

Let’s begin by recalling what we mean by the range of a function. Just as the domain is the set of possible inputs to our function, the range is the set of possible outputs. In other words, it’s the set of 𝑦-values we achieve when the domain of 𝑥-values have been substituted into the function. This means that graphically we’re looking at the spread of values in the 𝑦-direction to help us calculate the range of the function.

Looking at the graph, we see that the values of 𝑦 begin at negative one. And that’s when we input 𝑥-values less than or equal to four. Then at 𝑥 equals four, the values of 𝑦 steadily increase, and this arrow here tells us that the increase to ∞. We can therefore say that the range, the set of possible outputs, is all values of 𝑦 greater than or equal to negative one. To use set notation to define the same interval, we use the left-closed right-open interval from negative one to ∞. Note that the round bracket tells us that ∞ isn’t really a defined number. And so the range of this function, which is the set of possible 𝑦-values, is the left-closed right-open interval from negative one to ∞.

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