Question

The graph represents a function with the form f(x) = asin(bx + c).

On a coordinate plane, a function has a maximum of 6 and minimum of negative 6. It completes one period at StartFraction 2 pi Over 3 EndFraction. It decreases through the y-axis at (0, 2).

Which values of a, b, and c are possible?

a = 6, b = 1, c = StartFraction pi Over 3 EndFraction
a = 6, b = 3, c = pi
a = 3, b = 1, c = StartFraction pi Over 3 EndFraction
a = 3, b = 6, c = pi

Answer 1

Answer:

a=6, b=3, c=pi

Step-by-step explanation:

Got it right on edge

Answer 2

Using sine function concepts, it is found that possible values for a, b and c are given by:

• $a = 6, b = 3, c = \pi$

The standard sine function is given by:

$y = a\sin{(bx + c)}$

In which:

• The amplitude is 2a.

• The period is $\frac{2\pi}{b}$.

• The horizontal shift is c.

In this problem:

• Maximum of 6 and minimum of negative 6, hence the amplitude is 12, that is, $2a = 12 \rightarrow a = 6$.

• The period is of $\frac{2\pi}{3}$, hence $\frac{2\pi}{3} = \frac{2\pi}{b} \rightarrow b = 3$.

• It passes through the y-axis at (0,2), which is one third of the maximum. Considering the shift, we have that $c = \pi$.

You can learn more about the sine function at https://brainly.com/question/16818112