Question

The function below was generated using an equation of the form f(x) = asin(bx - c).

Find a, b, and c for the function such that the graph of f matches the figure.

A) a = 3, b = -2, c = π
B) a = 2, b = 3, c = -π
C) a = 3, b = 2, c = -π
D) a = 2, b = -3, c = π

Answer 1

The function such that the graph of f matches the figure is:

C) a = 3, b = 2, c = -π.

Step-by-step explanation:

The given function is in the form
`\(f(x) = a\sin(bx - c)\)`, which represents a sinusoidal function. In this equation:

`- \(a\)` determines the amplitude,

`- \(b\)` determines the frequency,

`- \(c\)` determines the phase shift.

Comparing the given function to the standard form, we can make the following observations:

- Amplitude (a): The amplitude is the distance from the axis of symmetry to the maximum or minimum point on the graph. Looking at the figure, it appears that the amplitude is 3.

- Frequency
`(\(b\))`: The frequency is related to how many cycles occur within a given interval. The figure suggests that the frequency is 2.

- Phase Shift
`(\(c\)):` The phase shift is a horizontal shift to the left or right. Based on the figure, it seems that there is a shift of
`\(-\pi\).`

Therefore, the correct choice is C) a = 3, b = 2, c = -π, as it satisfies the observed amplitude, frequency, and phase shift in the given graph of the function.