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 $[-1,1]+\frac{\pi}{2}\approx[0.57,2.57]$ 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 :)