# What is the range of y=-2sin(x+pi)-3

Linda Peters 2022-09-26 Answered
What is the range of $y=-2\mathrm{sin}\left(x+\pi \right)-3$?
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## Answers (1)

efterynzl
Answered 2022-09-27 Author has 12 answers
In the function $y=\mathrm{sin}\left(b\left(x+c\right)\right)+d$, the two parameters that will influence the range are a and d, which are the amplitude and vertical transformation, respectively.
The function $y=\mathrm{sin}x$ has an amplitude of 1 and a vertical transformation of 0, for example. Since the sine function rotates around the centre line which will be at y=0 (due to the vertical transformation), the range will be $-1\le y\le 1$.
With our function, the amplitude is |-2|=2 and the vertical transformation brings the centre line down to y=-3. Hence, the minimum values will be y=-3-2=-5 and our maximum values will be y=-3+2=-1
The range is therefore -$5\le y\le -1$
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