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mathdad
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Find the oblique asymptote of f(x) = (x^2 - 16)/(x - 4). I need the steps not the solution.
greg1313 said:f(x) simplifies to x + 4, which is the oblique asymptote of f(x).
skeeter said:The given rational function does not have an oblique asymptote ... it has a point discontinuity at the point (4,8)
greg1313 said:My mistake. It is equivalent to the line y = x + 4, with a discontinuity at x = 4 (where the denominator is zero).
RTCNTC said:You are saying that at x = 4, there is discontinuity. In other words, there is a hole in the graph of the function at the point (4, 8), right?
RTCNTC said:Why is an oblique asymptote called a slant asymptote?
An oblique asymptote is a type of asymptote that occurs when a function approaches a line at infinity, but does not intersect or touch the line. This line is typically slanted or tilted, and is often referred to as a "slant asymptote".
To find the equation of an oblique asymptote, you must first determine the degree of the numerator and denominator of the function. Then, you can use long division or synthetic division to divide the numerator by the denominator. The resulting quotient will be the equation of the oblique asymptote.
Yes, it is possible for a function to have more than one oblique asymptote. This can occur when the function has a complex or multi-part structure, such as a rational function with multiple terms in the numerator and denominator.
To graph an oblique asymptote, you must first plot the points of the function on a coordinate plane. Then, use the equation of the oblique asymptote to draw a dotted line that extends infinitely in both directions. Finally, plot additional points on the function to show how it approaches but does not touch the asymptote.
No, by definition, an oblique asymptote does not intersect with the function. If the function and the asymptote were to intersect, they would no longer be considered asymptotes. However, the function may approach the asymptote as closely as desired, making it appear as though they intersect.