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General functions practice

Identifying functions from graphs worksheets

Apply the vertical line test to eight finite graph relations. Choose lines, polynomials, special curves, horizontal parabolas or rotated curves, with balanced endpoints and a separate key.

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Imagine moving a vertical line across each graph. Circle Yes if it never meets the curve more than once; otherwise circle No.

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Move a vertical line across the curve

Each sheet contains eight finite graph relations with balanced curve categories and endpoint combinations. Lines, polynomial turns, waves, horizontal parabolas and rotated curves require the same one-output test.

The key repeats each graph and gives the exact Yes or No classification. Open endpoints remain excluded from the relation.

Learning objective

What this activity builds

Decide whether every vertical line meets a graphed relation at most once.

Worked example

A sideways parabola has vertex (−1, 1) and endpoints (−3, 0) and (−3, 2). Is it a function?

No.

The vertical line x = −3 meets the graph at two different y-values, so one input has two outputs.

Teaching notes

Make the practice count

  • Move the test line from left to right.
  • Count intersections with the curve, not the grid.
  • Open endpoints are excluded points.
  • A turning graph can still be a function.
  • One vertical line with two intersections proves a nonfunction.

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Math SheetNameScore/ 8TeacherDateIdentifying Functions from GraphsUse the vertical line test. Decide whether each graph represents a function.1.-5-5-4-4-3-3-2-2-1-1001122334455xyFunction?Yes / No2.-5-5-4-4-3-3-2-2-1-1001122334455xyFunction?Yes / No3.-5-5-4-4-3-3-2-2-1-1001122334455xyFunction?Yes / No4.-5-5-4-4-3-3-2-2-1-1001122334455xyFunction?Yes / No5.-5-5-4-4-3-3-2-2-1-1001122334455xyFunction?Yes / No6.-5-5-4-4-3-3-2-2-1-1001122334455xyFunction?Yes / No7.-5-5-4-4-3-3-2-2-1-1001122334455xyFunction?Yes / No8.-5-5-4-4-3-3-2-2-1-1001122334455xyFunction?Yes / Nomath-sheet.comPage 1 / 1

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