how to find the period, amplitude, and vertical shift of a sinusoidal graph. please explain in the simplest way possible, t

Step-by-step explanation:

a) period is the length of one cycle  ( one full squiggle ) If you are lucky and the graph is on exact numbers.. at a high point and to the next high point.. then just take that horizontal distance,  that's one period  also if it's not  you could find the period, T,  by using  T = 2pi / k    where k is a number that represents how fast , or how many times the wave cycles in one second or some other amount of time.  

b) Amplitude is a number that goes right before the sinusoid, which is multiplied by it because,  sin , cos,  are at max 1 or at min -1  

c)  vertical shift is what is added , for upwards shift... before or after the                      sinusoid  ie  sin , cos,  ect ect.

does this help?

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is