which function will have a y - intercept at -1 and an amplitude of 2?\n○ (f(x)=-sin(x)-1)\n○…

Answer:

B. $f(x)=-2\sin(x)-1$

Explanation:

Step1: Recall y - intercept formula

The y - intercept of a function $y = f(x)$ is found by setting $x = 0$, i.e., $y=f(0)$.

Step2: Recall amplitude formula

For a function of the form $y = A\sin(x)+k$ or $y = A\cos(x)+k$, the amplitude is $|A|$.

Step3: Check option A

For $f(x)=-\sin(x)-1$, when $x = 0$, $f(0)=-\sin(0)-1=- 0 - 1=-1$, and amplitude $|A| = |-1|=1\neq2$.

Step4: Check option B

For $f(x)=-2\sin(x)-1$, when $x = 0$, $f(0)=-2\sin(0)-1=-2\times0 - 1=-1$, and amplitude $|A| = |-2| = 2$.

Step5: Check option C

For $f(x)=-\cos(x)$, when $x = 0$, $f(0)=-\cos(0)=-1$, and amplitude $|A| = |-1|=1\neq2$.

Step6: Check option D

For $f(x)=-2\cos(x)-1$, when $x = 0$, $f(0)=-2\cos(0)-1=-2\times1 - 1=-3\neq - 1$.