Question Video: Finding the Domain and Range of a Cubic Function given Its Graph Mathematics

Video Transcript

Find the domain and range of the function 𝑓 of 𝑥 equals 𝑥 minus one cubed in all reals.

We’ve already been given the graph of this function, 𝑥 minus one cubed. So now we just need to think about what the domain and range are. When we have a graph, the domain is represented by the set of possible 𝑥-values and the range is the set of all possible 𝑦-values. It’s important to know that when we have this type of graph, we know that they continue in both directions. While we’re only seeing a bit of this function, from 𝑥 negative two to 𝑥 positive three, we know that it continues in both directions. The same thing is true for the 𝑦-values. We’re only seeing 𝑦-values up to positive 10 and down to negative 10.

However, this function continues outside of this window on our graph. In this case, we have no limits on our domain or range. The domain can be all real numbers, and the range can be all real numbers. It’s also possible that we might want to write this in interval notation instead of in set notation. The interval of the domain would be written as negative ∞ to ∞. And in this case, the same thing will be true for the range interval, all real numbers or values from negative ∞ to positive ∞.

With the interval notation here, it’s important to note that we use the round brackets when we are not including what is on the end. So what these say is that we want to go up to ∞ but not including ∞.