# How do you translate the graph of y=sinx-2?

Mar 1, 2018

See explanation.

#### Explanation:

This function means that for every number ($x$) you insert, you will be getting its sine ($\sin$) minus 2 ($- 2$).

Since each sine cannot be less than $- 1$ and more than $1$
($- 1 \le \sin \le 1$) and $2$ is always subtracted, you will be always getting a certain range of numbers (Range $= \left[- 3 , - 2\right]$).

Hence, the shape of the function is such than only take certain numbers.

The function will always be under the $x ' x$ axis, because highest possible value of $\sin x$ is $1$ and $2$ is always subtracted, so the function will always be equal to a negative value.

graph{y = sinx - 2 [-10, 10, -5, 5]}

I hope this makes sense to you.