What is the general equation of a sine function with an amplitude of 2, a period of Pi and a horizontal shift of Pi units? y = 2 sine (2 (x minus pi)) y = 2 sine (4 (x + pi)) y = sine (0.5 (x minus pi)) y = sine (2 (x + pi))

The general equation of the sine function is

The standard general equation of a sine function is represented as,

where, A represents the amplitude, B is the frequency, D is vertical shift and  C is the  phase shift.

Given that, amplitude of 2, a period of and a horizontal shift of

Therefore, general equation of sine function is,

Learn more:

link

The general equation of the sine function is;

y = 2 sine(2(x - π))

Step-by-step explanation:

Mathematically , the general equation of a sine function(sinusoid) can be written as;

y = A sin (B(x-C)) + D

where, A represents the amplitude

B is the frequency , where period = 2 π/B

D is vertical shift

C is the horizontal or phase shift

From the question, we have the following;

Amplitude of 2(A) ,

Period = π

Since Period = 2 π/B

This means that π = 2 π/B

Dividing both sides by π ; B = 2

Horizontal shift = π units = C

Plugging these values, we have

y = 2 sine(2(x - π))

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0