Linda Peters

2022-09-26

What is the range of $y=-2\mathrm{sin}(x+\pi )-3$?

efterynzl

Beginner2022-09-27Added 12 answers

In the function $y=\mathrm{sin}(b(x+c))+d$, 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 -$5\le y\le -1$

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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