Question

3. Which of the following is the graph of (x - 2)2 + (y + 1)2 = 9?

А.
с.
ТУ
В.
АУ
D.
БУ
о
-
А
B
Оа
Oь
Ос
Od
C С
D

Answer 1

The function given has the following form:

`y=A\cos (B(x+C))+D`

In this functions we have that:

• A is the amplitude.

,

• The period is 2pi/B

,

• Phase shift (horizontal translation) is C (to the left is C is positive.

,

• Vertical shift is D.

Now, we need to remember that the cosine function has a graph:

Now, in our function:

`y=2\cos (x-(\pi)/(2))-1`

Comparing with the general cosine above we conclude that:

• The amplitude is 2.

,

• The phase shift is pi/2 to the right.

,

• The vertical shift is 1 down.

,

• The period is 2pi.

Then the graph is:

Comparing with the options we conclude that the answer is B.