Graph one complete cycle of each of the following. In each case, label the axes accuratelyand identify the vertical translation for each graph. y = 6 - sin x
Graph one complete cycle of each of the following. In each case, label the axes accurately
and identify the vertical translation for each graph.
y = 6 - sin x
we have to graph the one complete cycle of the function y=6-sinx.
the equation of the given function can be written as:
as we know that if we have a function y=f(x) then the equation of the function shifted at (h,k) is given by:
y-k=f(x-h)
therefore the equation is the equation of the function y=-sinx shifted at a point.
let the point at which the function is shifted be (h,k).
therefore to find the value of h and k compare the equation with the equation
therefore, h=0 and k=6.
therefore the function y=6-sinx is the function y=-sinx shifted at (0,6).
therefore the graph of the function y=6-sinx will be obtained by translating the function y=-sinx vertically upwards by 6 unit.
the function y=6-sinx has a period and amplitude same as that of the function y=-sinx .
therefore the period of the function y=6-sinx has an amplitude '1' and period ''.
the graph of the function y=6-sinx and y=-sinx for one complete cycle is:
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