the graph of y= 6cos (x-2) – 3 is obtained by shifting the graph of y=6 cos x-3 horizontally 3 units to the right. true or false?

Question

the graph of y= 6cos (x-2) – 3 is obtained by shifting the graph of y=6 cos x-3 horizontally 3 units to the right. true or false?

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Ayla 2 weeks 2021-11-25T00:23:44+00:00 2 Answers 0

Answers ( )

    0
    2021-11-25T00:24:55+00:00

    Answer:

    The given statement is a false statement.

    Step-by-step explanation:

    We know that the transformation of the type:

    f(x) to f(x+k)

    is a horizontal shift of the graph.

    The graph is shifted k units to the right if k is negative and if k is positive then the graph is shifted k units to the left.

    Here we have the graph as:

                    y=6\cos (x)-3

    and the translated graph is given by:

           y=6\cos (x-2)-3

    This means that:

    f(x) → f(x-2)

    i.e. the graph is shifted horizontally 2 units to the right ( since k=2 is positive )

    0
    2021-11-25T00:25:32+00:00

    Answer:

    false.

    Step-by-step explanation:

    Given the function g(x) = f(x − k), can be sketched f(x) shifted k units horizontally. if k is negative, the function is shifted k units to the left.

    Given the function g(x) = f(x) + k, we can say that the function is translated vertically upwards k times. If k is negative, the function is translated vertically downwards k times.

    In this case, the function is translated two units to the right and 3 units down because the number “-3” is negative.

    So it’s false. The graph is translated three units downwards and 2 units to the right.

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