f(x) = 5/x+7 -6
A; x = -7 and y = 6
B: x = 7 and y = 6
C: x = -7 and y = -6
D: x = 5 and y = -6
5/(x + 7) - 6
The asymptotes of a function are the values that will make either the x or y undefined at a particular point. The first part is easy. We see that
y = 5 / (x + 7) - 6
This function is undefined when x = -7 because that makes the denominator 0 and any function with a 0 in the denominator is undefined. So the equation for our vertical asymptote is x = -7.
Finding the horizontal asymptote is a bit more complicated because we must put this equation in terms of y.
To do this we first bring the -6 to the y side by adding 6 to both sides. This gives us:
y + 6 = 5 / (x + 7)
We may now divide both sides by 5, to get:
(y + 6) / 5 = x + 7
And finally subtract 7 from both sides:
x = ((y + 6) / 5) - 7
Since this is the inverse of an equation, we must find what will give us 0 in the numerator. In this case, y = -6 gives us a 0.
So the answer is x = -7, y = 6, which is option A
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