What are the equations of the asymptotes of y=−1.6x+0.3−3.4?
A. x=0.3 and y=3.4
B. x=−0.3 and y=3.4
C. x=0.3 and y=−3.4
D. x=−0.3 and y=−3.4
Which of the following hyperbolas has a center at (−2,3)?
A. y=4x+3+2
B. y=4x+2+3
C. y=4x−2+3
D. y=4x+3−2
your equations make no sense to me
To find the equations of the asymptotes of a given function, you need to consider its behavior as x tends to positive or negative infinity.
For the equation y = -1.6x + 0.3 - 3.4, we can rewrite it in the form y = mx + b, where m is the slope and b is the y-intercept.
In this case, the slope is -1.6 and there is no y-intercept because the equation is already in y = mx + b form.
Since there is no y-intercept, the equation represents a slant asymptote. The slant asymptote has the equation of the form y = mx + c, where m is the slope and c is the y-value at which the graph intersects the y-axis.
To find the y-value at which the graph intersects the y-axis, substitute x = 0 into the equation:
y = -1.6(0) + 0.3 - 3.4 = -3.1
Therefore, the equation of the slant asymptote is y = -1.6x - 3.1.
As for the hyperbolas, the standard form of a hyperbola with a center at (h,k) is given by (x - h)^2 / a^2 - (y - k)^2 / b^2 = 1, where a and b are the lengths of the semi-major and semi-minor axis, respectively.
For the given options, let's rewrite them in the standard form and check if the center matches:
Option A: y = 4x + 3 + 2 => y = 4x + 5
Option B: y = 4x + 2 + 3 => y = 4x + 5
Option C: y = 4x - 2 + 3 => y = 4x + 1
Option D: y = 4x + 3 - 2 => y = 4x + 1
Comparing the equations with the standard form, we can see that options A and B have the same equation, y = 4x + 5.
Therefore, the hyperbola with a center at (-2, 3) is represented by the equation y = 4x + 3 + 2, which corresponds to option A.