Question Video: Determining the Domain and Range of a Constant Function given Its Graph Mathematics

Determine the domain and range of the function 𝑓(π‘₯) = βˆ’4.

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Video Transcript

Determine the domain and range of the function 𝑓 of π‘₯ equals negative four.

In the image, we’ve been given the graph of the function 𝑓 of π‘₯ equals negative four. In order to calculate the domain and range, we remember that the domain is represented by the π‘₯-values and the range is represented by the 𝑦-values on the graph. We also remember that the domain is the independent variable. It’s the variable we plug in to our function. We want to know what is the set of values that π‘₯ can be.

Now, on this graph, it might look like π‘₯ only goes from negative four to positive four. However, we recognize that this is a function that continues in both directions. To the right, π‘₯ would continue out to positive ∞ and to the left negative ∞. So how should we write this as a domain?

We could use this symbol that looks a little bit like an R. This symbol represents all real numbers. The domain for π‘₯ can be any real number.

What about the range? The range is a little bit different here. The range will be the 𝑦-values, that is, the distance up or down from zero. For every π‘₯-value in this function, 𝑦 is always negative four. 𝑦 does not change. And that means the only outcome, the only output of this function, is negative four. The range is the set of negative four. And so we can say for the function 𝑓 of π‘₯ equals negative four, the domain is all real numbers and the range is the set negative four.

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