What are the equations of the asymptotes of y=−1.6x+0.3−3.4?

which of the following hyperbolas has a center at (−2,3)?

1) D. x = -0.3 and y = -3.4

2) B.

Step-by-step explanation:

1) Given equation,

For vertical asymptote,

It is possible for the given function, if the denominator = 0

⇒ x + 0.3 = 0

⇒ x = -0.3

Now, for horizontal asymptote,

By substituting this in the given equation of the function,

We get,

Hence, the vertical and horizontal asymptote of the given function are x = -3.0 and y = -3.4 respectively.

⇒ Option D is correct.

2) If a function is defined as,

(x-h)(y-k) = a

Then (h,k) be the center of this function,

In option A,

Given function is,

⇒ The center of the function is (-3,2)

In option B,

Given function is,

⇒ The center of the function is (-2,3)

In option C,

Given function is,

⇒ The center of the function is (2,3)

In option D,

Given function is,

⇒ The center of the function is (-3,-2)

⇒ Thus, by the above explanation the function in option B has the center of (-2,3)