Consider a function graphed as a curved line segment traversing through the points $$(-2, 1)$$, $$(0, 3)$$, and $$(4, -5)$$. The domain is determined by finding all the $$x$$-values that correspond to a point on the graph. Since the graph extends horizontally from $$-2$$ to $$4$$, the domain in interval notation is $$[-2, 4]$$. The range is determined by finding all the $$y$$-values associated with the graph. The lowest vertical point is at $$-5$$ and the highest is at $$3$$, so the range in interval notation is $$[-5, 3]$$.

Claude

To find the range of a function from its graph, identify all the values of $$y$$ that correspond to a point on the graph. Visually follow a given $$y$$-value left or right horizontally; if this horizontal path intersects the graph of the function, then that specific $$y$$-value is mathematically included in the range.

Reading the Range of a Function from its Graph

https://openstax.org/details/books/intermediate-algebra-2e

OpenStax Intermediate Algebra

Consider a function whose graph is a curved line segment passing through the points $$(-5, -4)$$, $$(0, -3)$$, and $$(1, 2)$$. To find its domain, observe all the $$x$$-values that correspond to a point on the graph; the curve spans horizontally from $$-5$$ to $$1$$, so the domain is written in interval notation as $$[-5, 1]$$. To find its range, examine all the $$y$$-values associated with the graph; the curve spans vertically from its lowest point at $$-4$$ to its highest point at $$2$$, making the range $$[-4, 2]$$.

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