Problem preview

F-IF.7.b Warmup M3-024-A14-V02

Graph square-root, cube-root, absolute-value, step, and piecewise-defined functions.

Identify continuity or discontinuity at a point from graph features

Problem

What kind of continuity or discontinuity is shown by these graph features: an open circle at \((1,3)\) and a closed point at \((1,7)\)?

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There is a jump discontinuity at x = 1 because the graph shows two different y-values, 3 and 7, at the same x-value.

There is a removable discontinuity at x = 1 because the graph has an open circle at y = 3 but the actual function value is the closed point at y = 7.

There is a removable discontinuity at x = 3 because the open circle at y = 3 shows the missing value on the graph.

The graph is continuous at x = 1 because the closed point at (1,7) shows the function is defined there.

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Curriculum context

Course: Math III
Standard: F-IF.7.b
Category: Functions
Domain: Interpreting Functions
Objective: Graph square-root, cube-root, absolute-value, step, and piecewise-defined functions.
Problem type: Identify continuity or discontinuity at a point from graph features