Florida B.E.S.T. MA.912.C.1.10
The Standard
Given the graph of a function, identify whether a function is continuous at a point. If not, identify the type of discontinuity for the given function.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students examine a graph near a given x-value and decide whether the graph passes through that point without a break. If there is a break, they classify it as removable, jump, or infinite.
What Mastery Looks Like
- Students check the function value, the left-hand and right-hand limits, and whether all three agree. When continuity fails, they correctly label the break as removable, jump, or infinite.
Common Misconceptions
- Students may call every open circle a removable discontinuity without checking the filled point at the same x-value. They may confuse a jump with an infinite discontinuity. They may also ignore whether the left-hand and right-hand limits agree.
How to Assess It
- Show a graph with a hole at x = 2 and a filled point at a different height. Ask, “Is the function continuous at x = 2? Name the discontinuity and justify your answer.”
Lesson moves
Ways to Teach It
Give groups graph cards and a sorting mat labeled continuous, removable, jump, and infinite, then require one written reason per card.
Display a graph and ask, “What must be true about the function value and both one-sided limits for continuity at x = 3?”
Play Continuity Relay: teams classify one marked point, record evidence, then pass the graph to the next teammate for checking.
Use a temperature graph with a missing reading, a sudden change, and an unbounded model to connect each break type to data.
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Related Standards
- MA.912.C.2.9
Demonstrate and use the relationship between differentiability and continuity.
- MA.912.F.1.1
Given an equation or graph that defines a function, determine the function type. Given an input-output table, determine a function type that could represent it.
- MA.912.C.1
Develop an understanding for limits and continuity. Determine limits and continuity.
- MA.8.F.1.2
Given a function defined by a graph or an equation, determine whether the function is a linear function. Given an input-output table, determine whether it could...
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