Problem preview
F-IF.7.b Warmup M3-024-A14-V01

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: the left and right pieces meet at the closed point \((2,5)\)?

Big Picture

What this problem is really about

Continuity at the junction requires three quantities to agree: the value approached from the left, the value approached from the right, and the function’s actual value there. Read each one separately from the two pieces and the filled point, then compare them. A closed point alone is not enough unless both sides approach that same height.

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Four variants of this problem type
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