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

Nov 19, 2016

The range is -5 ≤ y ≤ -1

#### Explanation:

In the function $y = \sin \left(b \left(x + c\right)\right) + d$, the two parameters that will influence the range are $a$ and $d$, which are the amplitude and vertical transformation, respectively.

The function $y = \sin x$ 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 ≤ y≤ 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 ≤ y≤ -1.

Hopefully this helps!