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TMUA 2017 · Paper 1 · Question 18 of 20

TMUA 2017 Paper 1 Question 18

Exponentials and logarithms — Logarithm graphs · translation as a stretch. Try it first; the answer and a full worked solution are below.

TMUA 2017 · Paper 1Exponentials and logarithmsLogarithm graphs · translation as a stretch6 options
The graph of y = log10 x is translated in the positive y-direction by 2 units.

This translation is equivalent to a stretch of factor k parallel to the x-axis.

What is the value of k?

  1. A0.01
  2. Blog10 2
  3. C0.5
  4. D2
  5. Elog2 10
  6. F100
Show the answer and worked solution
answer · A
  1. A0.01
  2. Blog10 2
  3. C0.5
  4. D2
  5. Elog2 10
  6. F100
The translated curve is y = log10 x + 2 = log10(100x). A stretch of factor k parallel to the x-axis replaces x by xk, giving y = log10xk. Matching the two, 1k = 100, so k = 0.01. The stretch is a squash towards the y-axis, which is why the answer is small rather than 100.