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    Mathematics
    Grade-8
    Easy

    Question

    Match the function g(x) = (x – 4)2 - 6 to the graph.

    hintHint:

    We will substitute the points on given graphs to find which graph represents the given function.

    The correct answer is:

      GIVEN-
      g(x) = (x – 4)2 - 6
      TO FIND-
      Graph of the given function.
      SOLUTION-
      >> Option b is eliminated because it has point (-5,-5) on the graph.
      However, as per the given function-
      g(x) = (x – 4)2 - 6
      ∴ g(x) = (-5 - 4)2 - 6
      ∴ g(x) = (-9)2 - 6
      ∴ g(x) = 81 - 6
      ∴ g(x) = 75
      Since, (-5,-5) does not satisfy the given function, it is not the correct answer.
      >> Option c is eliminated because it has point (-5,5) on the graph.
      Hence, option c is also eliminated,
      >> Option d is eliminated because it has point (5,-3) on the graph.
      However, as per the given function-
      g(x) = (x – 4)2 - 6
      ∴ g(x) = (5 - 4)2 - 6
      ∴ g(x) = (1)2 - 6
      ∴ g(x) = 1 - 6
      ∴ g(x) = -5
      Since, (5,-5) does not satisfy the given function, it is not the correct answer.
      Hence, option a is the correct answer.
      FINAL ANSWER-
      Option 'a' is the correct answer to the given question.

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