Question

Find a function of the form y=Asin(kx)+C or y=Acos(kx)+C whose graph matches the function shown. ( in the picture)

Answer 1

Answer:

Your answer is: y = -3cosπ /2 - 3

​  

Step-by-step explanation:

We learned this last semester in pre calculus lol XD

Answer 2

Answer:

The required function is $y=\sin\left(\frac{\pi}{7}x\right)-3$.

Step-by-step explanation:

From the given graph it is clear that the value of function is not extreme at x=0, so the required function is a sine function.

The general form of a sine function is

$y=A\sin(kx)+C$                 ..... (1)

where, A is amplitude, $\frac{2\pi}{k}$ is period and C is midline.

From the given graph it is clear that the maximum value of the function is -2 and minimum value of the function is -4.

$Amplitude=\frac{Maximum-Minimum}{2}$

$Amplitude=\frac{-2-(-4)}{2}=1$

$Midline=\frac{Maximum+Minimum}{2}$

$Midline=\frac{-2+(-4)}{2}=-3$

The function complete a cycle in 14 units, so period of the function is 14.

$\frac{2\pi}{k}=14$

$\frac{2\pi}{14}=k$

$\frac{\pi}{7}=k$

Substitute A=1, $k=\frac{\pi}{7}$ and C=-3 in equation (1).

$y=(1)\sin(\frac{\pi}{7}x)+(-3)$

$y=\sin\left(\frac{\pi}{7}x\right)-3$

Therefore the required function is $y=\sin\left(\frac{\pi}{7}x\right)-3$.