Using the figure below, determine the range of 𝑓 of 𝑥.
So the first thing we need to do with this question is understand what range means and, more specifically, what the range of a function is. Well, when we’re dealing with functions, we often hear of the range and the domain. The range, what we’re looking for in this question, of a function is the complete set of all possible resulting values of the dependent variable 𝑦. What this means is, if we have a set of values of 𝑥, then the range of possible outcomes when using these values of 𝑥 for 𝑦 is the range.
And if we think about the domain — I know it’s not what we’re finding in this question but it’s useful to know. Well, the domain of a function is the complete set of possible values of the independent variable, so 𝑥. So it’s the 𝑥-values that we can put into a function. And you might think, “Well, won’t that just be every value?” But it won’t be. For instance, if 𝑥 was on the bottom of a fraction, so it is the denominator, we could say that 𝑥 won’t be able to be zero. Because then, we wouldn’t have a function that worked or gave a value that we could use.
Okay, so now we have our definitions. Let’s determine the range of our function. Well, because it’s the range that we’re interested in, it’s the 𝑦-axis or 𝑦-values that we’re looking for. So we can see that our first value is gonna be negative two. Our next possible value of 𝑦 is negative one. Well, the next possible value is actually where the point meets the 𝑥-axis. So therefore, it’s going to be at zero. So 𝑦 is equal to zero. So our output of our function would be zero at that point. Then we have one, and then we have two.
So what we’ve done is put each of these values or elements inside of our set notation. Which is these sorts of curly brackets which are sometimes called braces. So therefore, we can say that the range of 𝑓 of 𝑥 is negative two, negative one, zero, one, and two.