the graph of which function passes through (0,3) and has an amplitude of 3?\n$f(x)=sin(x)+3$\n$f(x)=cos(x)+3$…
the graph of which function passes through (0,3) and has an amplitude of 3?\n$f(x)=sin(x)+3$\n$f(x)=cos(x)+3$\n$f(x)=3sin(x)$\n$f(x)=3cos(x)$
Answer
Explanation:
Step1: Recall amplitude formula
For functions of the form $y = A\sin(x)+k$ or $y = A\cos(x)+k$, the amplitude is $|A|$.
Step2: Check amplitude of each option
- For $f(x)=\sin(x)+3$, $A = 1$, amplitude is $1$.
- For $f(x)=\cos(x)+3$, $A = 1$, amplitude is $1$.
- For $f(x)=3\sin(x)$, $A = 3$, amplitude is $3$.
- For $f(x)=3\cos(x)$, $A = 3$, amplitude is $3$.
Step3: Check if the function passes through (0,3)
- For $f(x)=3\sin(x)$, when $x = 0$, $f(0)=3\sin(0)=0\neq3$.
- For $f(x)=3\cos(x)$, when $x = 0$, $f(0)=3\cos(0)=3\times1 = 3$.
Answer:
$f(x)=3\cos(x)$