Calculus
Graphing from Function Properties worksheets
Analyze exact intercepts, critical points, inflection points, behavior intervals, concavity, and relative extrema before sketching a function.
Preview and downloadCalculus practice
Graphing Derivatives worksheets
Sketch derivative graphs from aligned polynomial, rational, and trigonometric function graphs, with an optional explicit equation.
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Use the graph of f to sketch f' on the aligned blank grid.
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Aligned axes, explicit windows, and separate rational branches make slope and shape claims visible rather than implied.
Learning objective
What this activity builds
Translate increasing, decreasing, stationary, and discontinuous behavior of f into a graph of f' on the same domain.
Worked example
If f(x)=x^2, what is the derivative graph?
The line f'(x)=2x.
The slopes of the parabola increase linearly, are zero at the vertex, and change from negative to positive.
Teaching notes
Make the practice count
- Align x-values between the two grids.
- Derivative zeros line up with horizontal tangents of f.
- Carry every pole or hole into the derivative domain.
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Customize the practice
Choose your options, update the preview, then download the exact same pages.
Choose a nonempty set of function families. Every graph uses a stated window and keeps discontinuous branches separate.
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