Determine the range of the function represented by the graph below.
Determine the range of the function
represented by the graph below.
We begin this question by recalling
that the range of a function 𝑓 is the set of all its outputs or 𝑦-values. We need to find all the 𝑦-values
that are represented by the curve. Our graph is in the shape of a
parabola. And it appears that the function is
quadratic. It has a maximum at the point with
coordinates negative seven, one. This means that 𝑓 of negative
seven is equal to one, and the maximum value of the function is one. There is no 𝑥-value such that 𝑓
of 𝑥 is greater than one.
Looking at the graph, it does
appear that the parabola takes on all values less than or equal to one. And we can therefore conclude that
the range of the function is the set of real 𝑦-values such that 𝑦 is less than or
equal to one. This can also be written using
interval notation as the left-open, right-closed interval from negative ∞ to