Question

describe the transformation of $f(x)$ to $g(x)$
$\boldsymbol{f(x)=\sin x}$
$\boldsymbol{g(x)}$
a $f(x)$ is shifted up 1 unit to $g(x)$
b. $f(x)$ is shifted up $\frac{1}{2}$ units to $g(x)$
c. $f(x)$ is shifted down 1 unit to $g(x)$
d. $f(x)$ is shifted down $\frac{1}{2}$ units to $g(x)$

Explanation:

Compare the vertical positions of \(f(x) = \sin x\) and \(g(x)\). The graph of \(g(x)\) is consistently below \(f(x)\) by 1 unit (e.g., \(f(0)=0\) vs \(g(0)=-1\)). This indicates a vertical shift down by 1 unit.

Answer:

C. \(f(x)\) is shifted down 1 unit to \(g(x)\)