Respuesta :

Answer:

The graph that matches the equation y = 2sin(x – π) + 2 is D

Step-by-step explanation:

To determine which graph matches the given equation y = 2sin(x – π) + 2. We will determine the values of y for range of values of x from -2π to 5π.

When x = -2π

From

y = 2sin(x – π) + 2

Then

y = 2sin(-2π – π) + 2

y = 2sin(-3π) + 2

(NOTE: π = 180°)

∴ y = 2sin(-540) + 2

y = 2(0) +2

y = 0 + 2

y =2

When x = -π

Then

y = 2sin(-π – π) + 2

y = 2sin(-2π) + 2

y = 2sin(-360) + 2

y = 2(0) +2

y = 0 + 2

y =2

When x = 0

Then

y = 2sin(0 – π) + 2

y = 2sin(-π) + 2

y = 2sin(-180) + 2

y = 2(0) +2

y = 0 + 2

y =2

When x = π

Then

y = 2sin( π– π) + 2

y = 2sin(0) + 2

y = 2(0) +2

y = 0 + 2

y =2

When x = 2π

y = 2sin(2π – π) + 2

y = 2sin(π) + 2

y = 2sin(180) + 2

y = 2(0) +2

y = 0 + 2

y =2

When x = 3π

y = 2sin(3π – π) + 2

y = 2sin(2π) + 2

y = 2sin(360) + 2

y = 2(0) +2

y = 0 + 2

y =2

When x = 4π

y = 2sin(4π – π) + 2

y = 2sin(3π) + 2

y = 2sin(540) + 2

y = 2(0) +2

y = 0 + 2

y =2  

When x = 5π

y = 2sin(5π – π) + 2

y = 2sin(4π) + 2

y = 2sin(720) + 2

y = 2(0) +2

y = 0 + 2

y =2

The only graph that corresponds to the tested values of x is the last graph (D)

Hence, the graph that matches the equation y = 2sin(x – π) + 2 is D.

The graph of the given equation is given by option D) and this can be determined by using the rules of transformation.

Given :

Equation  --  [tex]y = 2\sin(x-\pi)+2[/tex]

The following steps can be used in order to determine the graph that represents the given equation:

Step 1 - Write the given equation.

[tex]y = 2\sin(x-\pi)+2[/tex]

Step 2 - Now, draw the graph of (sin x) and then translate it by a factor of [tex]\pi[/tex] in the right direction. So, the graph obtained is the graph of [tex]\sin(x-\pi)[/tex].

Step 3 - Now, stretch the graph of [tex]\sin(x-\pi)[/tex] by a factor of 2. So, the graph obtained is the graph of [tex]2\sin(x-\pi)[/tex].

Step 4 - Now, translate the graph of [tex]2\sin(x-\pi)[/tex] by a factor of 2 in the upward direction. So, the graph obtained is the graph of [tex]2\sin(x-\pi)+2[/tex].

Therefore, the correct option is D).

For more information, refer to the link given below:

https://brainly.com/question/14375099

Otras preguntas