Question

Write an equation for a function with the given characteristics. a sine curve with a period of 4, an amplitude of 2, a left phase shift of /2, and a vertical translation down 4 units.

Answer 1

The equation for the function is f(x) = 2 * sin((π/2) * (x + π/2)) - 4.

Explanation:

To write an equation for a function with the given characteristics, we can start with the general form of a sine function:

f(x) = A * sin(B * (x - C)) + D

Where:

A is the amplitude

B determines the period (B = 2π / period)

C determines the phase shift

D determines the vertical translation

Given the characteristics you provided:

Amplitude (A) = 2

Period = 4, so B = 2π / 4 = π/2

Phase shift (C) = -π/2 (left phase shift of π/2)

Vertical translation (D) = -4 units

Plugging in these values, the equation for the function is:

f(x) = 2 * sin((π/2) * (x + π/2)) - 4

Thus,

The equation for the function is f(x) = 2 * sin((π/2) * (x + π/2)) - 4.