The function f(x)is graphed above. Which of the graphs below represents the function g(x)=(x+1)^2

Question

The function f(x)is graphed above. Which of the graphs below represents the function g(x)=(x+1)^2

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Mia 1 month 2021-10-18T19:37:33+00:00 1 Answer 0 views 0

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    2021-10-18T19:39:27+00:00

    Answer:

    The function g(x) = (x + 1)² is represented by the graph Y

    Step-by-step explanation:

    The question presents the graph of the function x² above

    Therefore, for a function f(x) = x² at x = 0 y = 0

    For function g(x) = (x + 1)² when x = 0 g(x) = 1  Satisfied by graph W and Y

    Also we have g(x) =  (x + 1)² = x² + 2·x + 1  or g(x) = f(x) + 2·x + 1

    We find the minimum of the graph by differentiating and equating to zero as follows;

    \frac{\mathrm{d} (x + 1)^{2}}{\mathrm{d} x} = 2x +2 = 0

    Therefor, the minimum is at x = -1 satisfied by only graph Y

    Hence the graph that represents the function g(x) = (x + 1)² is the graph Y.

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