NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Graph transformations and parameters

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The graph of y = x is transformed by a vertical stretch by a factor of 3, followed by a vertical translation of 4 units down.

What is the y-coordinate of the point on the transformed graph that corresponds to x = 2?

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Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The original function is y = x. We are given a vertical stretch by a factor of 3, which means we multiply the output (y-value) by 3.
  2. After the vertical stretch, the new function becomes y = 3x.
  3. Next, a vertical translation of 4 units down is applied. This means we subtract 4 from the y-value.
  4. After the translation, the transformed function is y = 3x - 4.
  5. We are asked to find the y-coordinate when x = 2 on the transformed graph.
  6. Substitute x = 2 into the transformed equation: y = 3(2) - 4.
  7. Perform the multiplication: 3 × 2 = 6.
  8. Subtract 4 from 6: 6 - 4 = 2.
  9. The y-coordinate at x = 2 is 2.
  10. Check: original point (2,2) after stretch becomes (2,6), then down 4 units to (2,2). Correct.

Reference answer: 2

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