Answers
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).
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Mathematics Diagnostic Assessment
1
Todd forgot the first two numbers of his locker combination. The numbers can be any number 1 through 6. What is the
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OA.
OB.
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கான்
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It is given that:
The total cost of 5 doughnuts and 6 cookies at a bakery is $11.95.The cost of each cookie is $0.95.
The cost of 1 doughnut is x.
Total cost = $11.95
Total cost = 5(0.95) + 6x
11.95 = 5(0.95) + 6x
Or
5(0.95) + 6x = 11.95
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x = $1.2
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5(0.95) - 6x = 11.95
5(0.95) + 6x = 11.95
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Answers
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Answers
======================================================
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