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 ∞.