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05.05.2020 •
Mathematics
Determine o período e o conjunto imagem, construindo o gráfico de um período completo para cada função dada.a) por f(x) = 1+ 4 sen x.b) por f(x) = 2sen (x-3)
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Ответ:
The given functions are
The sine function has a standard period of
by definition. However, this might change if we use a factor as coefficient of the x-varible, but in this case we don't have that.
Therefore, the period of both trigonometric functions is
.
Now, the images of each function is the y-variable set values that defines each function.
So, the function
has an image defined by the set
. It's impotant to notice that the range of a standard function is [-1,1], however, in this case, the function was shifted 1 unit up and it was streched by a factor of 4, that's why the standard image changes to
.
About the second function
, the image set is
, because the function was streched by a factor of 2.
Additionally, the image attached shows the graph of the given functions.
Ответ: