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How do I determine the domain and the equation of the vertical asymptote with the equation f of x equals In parentheses x plus 2 end of parentheses minus 1?
The domain of the function f(x) = (x + 2)^-1 is whatever you choose it to be, except that the point x = -2 must be excluded.
If the domain comes up to, or straddles the point x = -2 then that is the equation of the vertical asymptote. However, if you choose to define the domain as x > 0 (in R), then there is no vertical asymptote.
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Determine the equation of any vertical asymptote and the value of x for any hole in the graph of the rational function fx x-2 over xsquared-x-2?
Asymptote's occur when your equation has a denominator of zero Holes may occur when your equation has both a numerator and denominator of zero So... The equation for the denominator equals zero is: x2-x-2 = 0 The equation for both the numerator and denominator equals zero is x - 2 = x2-x-2 = 0 For interests sake... lets solve it. ---- x2-x-2 = 0 (x+1)(x-2) = 0 x = -1, 2 x - 2 = x2-x-2 = 0 x - 2 = 0 x = 2 A vertical asymptote occurs at x = -1 A vertical asymptote or hole may appear at x = 2
When a vertical asymptote is reflected over the x axis what does it become?
It remains a vertical asymptote. Instead on going towards y = + infinity it will go towards y = - infinity and conversely.
All rational functions have more than one vertical asymptote?
false
If a function has a vertical asymptote at a certain x-value then the function is at that value?
Undefined
Does every undefined value of fx lead to a vertical asymptote?
No. For example, in real numbers, the square root of negative numbers are not defined.
