Mathematics
Grade10
Easy

Question

For a given pair f left parenthesis x right parenthesis equals cube root of 3 x minus 1 end root comma g left parenthesis x right parenthesis equals cube root of 9 x minus 1 end root the graph of g is a ___________ of the graph of f .

  1. Vertical stretch
  2. Vertical compression
  3. Horizontal stretch
  4. Horizontal compression

The correct answer is: Horizontal compression


    g left parenthesis x right parenthesis equals cube root of 9 x minus 1 end root equals cube root of 3 left parenthesis 3 x right parenthesis minus 1 end root equals f left parenthesis 3 x right parenthesis comma text  where  end text k equals 3 greater than 1
    g left parenthesis x right parenthesis equals f left parenthesis k x right parenthesis text  for  end text vertical line k vertical line greater than 1
    So, the graph of g is a horizontal compression of graph of f.

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