General functions
Inverse functions worksheets
Identify inverse pairs or find inverse functions in twelve original questions. Practice linear functions and powers with explicit domains, exact radicals and worked answers.
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Graphing inverse functions worksheets
Find and graph four inverse functions. Choose fractional or integer linear rules, lines through the origin, quadratic branches and cubic functions, with completed graph keys.
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Find the inverse formula by swapping x and y and solving for y. Plot the original function on its stated domain. Swap the coordinates of its points to draw the inverse.
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Swap the coordinates. Reflect the graph.
Each worksheet contains four questions with blank unit grids from −10 to 10 on both axes. Choose one or more of five families: fractional linear rules, integer linear rules, lines through the origin, quadratic branches and cubic functions.
When up to four families are selected, every selected family appears. With all five selected, four appear on each sheet; change the seed for a new selection. Quadratic questions explicitly choose the left or right branch so their inverse is a function.
The separate key shows the original curve as a solid line, the inverse as a dashed line and the reflection guide y = x in gray. It also prints the exact inverse formula, its domain and its range. Graphs stop at the visible grid boundary; that boundary is not a restriction on the mathematical domain.
Learning objective
What this activity builds
Connect an inverse formula to the reflection of a function graph across y = x, respecting its domain and range.
Worked example
Graph f(x) = (x − 2)² for x >= 2 and its inverse.
The inverse is 2 + √x, with domain x >= 0. Points (2, 0), (3, 1) and (4, 4) reflect to (0, 2), (1, 3) and (4, 4).
Use only the right branch of the parabola. Reflecting across y = x swaps coordinates, including the endpoint. The inverse range is y >= 2, matching the original domain.
Teaching notes
Make the practice count
- Begin with linear rules before introducing root graphs.
- Use the same unit scale on both axes.
- Draw the line y = x as a reflection guide.
- Swap both coordinates of several easy points.
- For a quadratic, plot only the branch allowed by the printed domain.
- Check that the inverse domain and range exchange the original range and domain.
- The key uses a solid original curve and a dashed inverse, so it also works in grayscale.
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