Question

Describe the transformation of f(x) to g(x). Pleaseee helllp thank youuuu!!!

Answer 1

The transformation set of
`y` values for function
`f` is
`[-1,1]` this is an interval to which sine function maps.

You can observe that the interval to which
`g` function maps equals to
`[-2,0]`.

So let us take a look at the possible options.

Option A states that shifting
`f` up by
`\pi/2` would result in
`g` having an interval
`[-1,1]+(\pi)/(2)\approx[0.57,2.57]` which is clearly not true that means A is false.

Let's try option B. Shifting
`f` down by
`1` to get
`g` would mean that has a transformation interval of
`[-1,1]-1=[-2,0]`. This seems to fit our observation and it is correct.

So the answer would be B. If we shift
`f` down by one we get
`g`, which means that
`f(x)=\sin(x)` and
`g(x)=f(x)-1=\sin(x)-1`.

Hope this helps :)