Calculus
Determining Continuity
Practice exact continuity intervals and one-sided-limit reasoning for piecewise, absolute-value, kinked-polynomial, and rational functions.
Preview and downloadCalculus practice
Determining Continuity from Graphs
Read completed graphs or sketch exact piecewise, absolute-value, kinked-polynomial, and rational functions before finding continuity intervals.
Ready-made English PDF · fixed settings
Customization below makes a separate PDF.
Fixed English ready-made files. Custom settings below apply only to the configured PDF.
Ready to print
Start with a ready-made worksheet
Find maximal open intervals where each graphed function is two-sided continuous.
Download the practice pages alone, or include a separate answer key or teacher model. Longer activities may use more than one page.
Customize this worksheetRead every graph feature
Open points, filled values, jumps, and vertical asymptotes reveal exactly where continuity intervals split.
Learning objective
What this activity builds
Use graph features to identify maximal open intervals of two-sided continuity without mistaking corners for breaks.
Worked example
Does an open circle always mean a vertical asymptote?
No. A finite open circle can be a removable hole or one side of a jump.
Compare the graph from both sides and check any filled point at the same x-coordinate.
Teaching notes
Make the practice count
- Trace each branch from left to right.
- Use filled points as actual function values.
- Keep continuous corners inside one interval.
Make it yours
Customize the practice
Choose your options, update the preview, then download the exact same pages.
Choose 4 or 8 problems, any retained function-family combination, and completed-graph or sketch-first student pages.
Enlarged pages scroll. PDF size stays the same.
A useful next step
Related activities
Calculus
Derivative-definition limit worksheets
Evaluate exact polynomial, reciprocal-power and trigonometric derivative limits at rational and pi-grid points.
Preview and download