the graph of which function passes through (0,3) and has an amplitude of 3?\no (f(x)=sin(x)+3)\no…

Explanation:

Step1: Recall amplitude formula

For functions of the form $y = A\sin(x)+k$ or $y = A\cos(x)+k$, the amplitude is $|A|$. We want $|A| = 3$. All options $f(x)=\sin(x)+3$, $f(x)=\cos(x)+3$ have amplitude $1$, so we can rule them out. We are left with $f(x)=3\sin(x)$ and $f(x)=3\cos(x)$.

Step2: Check point $(0,3)$

For $y = f(x)=3\sin(x)$, when $x = 0$, $y=3\sin(0)=0$. For $y = f(x)=3\cos(x)$, when $x = 0$, $y = 3\cos(0)=3\times1 = 3$.

Answer:

$f(x)=3\cos(x)$