Problem

Use the displayed continuous segment and discrete-point graph to determine and compare their domains and ranges. Explain how continuity or discreteness controls the included values.

Actual source graphs distinguishing the continuous and discrete functions or the stated function families.

Big Picture

What this problem is really about

Domain and range come from projecting a relation horizontally and vertically, but the graph’s inclusion type matters just as much as its endpoints. We’ll read x-values for domain and y-values for range, then decide whether values between the marked coordinates belong. Continuous pieces call for intervals, while isolated points call for explicit finite sets.

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Preview only

The line segment has domain [2,12] and range [0,5], and the discrete points have domain 2,4,6 and range 0,1,2 because the first numbers and second numbers are being compared in reverse.

The line segment has domain [0,5] and range [2,12], and the discrete points have domain [0,2] and range [2,6] because both graphs cover every value between their smallest and largest coordinates.

The line segment has domain [0,5] and range [2,12] because it includes all x- and y-values between its endpoints, while the discrete points have domain 0,1,2 and range 2,4,6 because only those listed coordinates are included.

The line segment has domain 0,5 and range 2,12, while the discrete points have domain 0,1,2 and range 2,4,6 because domain and range come only from the shown coordinates.

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Use the displayed continuous segment and discrete-point graph to determine and compare their domains and ranges. Explain how continuity or discreteness controls the included values.

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