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Question Video: Finding the Range of a Quadratic Function given Its Graph Mathematics • 9th Grade

Determine the range of the function represented by the graph below.

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Video Transcript

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 one.

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