Question

How do you shift and graph `y=-3+sinx`?

Answer 1

The period of `sin` is `2pi`.

The `-3` is applied to the result of `sin(x)` which affects the `y` value.

All of the points will be shifted down `3` units.

Rely on your knowledge of the unit circle to figure out the values of sin on the `x` and `y` axis.

`f(0)=-3+sin(0)=-3+0=-3 -> (0,-3)`

`f(pi/2)=-3+sin(pi/2)=-3+1=-2 -> (pi/2,-2)`

`f(pi)=-3+sin(pi)=-3+0=-3 -> (pi,-3)`

`f((3pi)/2)=-3+sin((3pi)/2)=-3-1=-4 -> ((3pi)/2,-4)`

`f(2pi)=-3+sin(2pi)=-3+0=-3->(2pi,-3)`

Enter the function into the calculator

Set the interval, XMIN and MAX , from `[0,2pi] -> 2pi=6.283185307`

Press the GRAPH button