Mathematics
Grade-8
Easy

Question

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

Hint:

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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