Why can horizontal asymptotes be crossed? - Physics Forums
Aug 5, 2007 · The main reason a function may cross its horizontal asymptote is because it has a removable discontinuity. This means that there is a point on the graph where the function is undefined, but it can be filled in with a single value to make the graph continuous. 2.
Describing behavior on each side of a vertical asymptote - Physics …
Jan 2, 2006 · The behavior on each side of a vertical asymptote can be described using limit notation. For example, if the asymptote is located at x=a, the limit of the function as x approaches a from the left side would be written as lim x→a- f(x) and the limit from the right side would be written as lim x→a+ f(x).
Horizontal asymptotes - approaches from above or below?
Feb 22, 2009 · For the vertical asymptote, x = 1/2, and that , while . Meanwhile, for the horizontal asymptote, there is one at y = -3. However, I do not know understand whether it approaches from above or below. This is how I tried to find it: As x --> -3 from the left, eg. x = -10, = = -0.81. therefore approaches from above, because -0.81 is greater than -3.
Oblique Asymptotes: What happens to the Remainder? - Physics …
Oct 24, 2011 · What happens to the remainder when finding an oblique asymptote? The remainder is the difference between the original function and the oblique asymptote. When finding an oblique asymptote, the remainder becomes 0, indicating that the function is getting closer and closer to the asymptote. 5.
Do we include asymptotes as critical points? - Physics Forums
Nov 30, 2007 · Yes, asymptotes can affect the domain and range of a function. Asymptotes can limit the values that the function can take, and therefore, impact the domain and range of the function. 4. Do we include vertical asymptotes as critical points? No, vertical asymptotes are not considered critical points because they do not occur on the graph of the ...
What is an asymptote and why doesn't parabola have one?
Oct 1, 2007 · A function f (x) has an asymptote if it "looks like" a straight line when x tends to . More precisely, if the distance tends to 0. A parabola doesn't have one. Suppose there was one (draw an arbitrary line in the same graph). Then, at some point, the parabola will rush past that line and keep going away from it, so it wasn't an asymptote.
Asymptote of a curve in polar coordinates - Physics Forums
Apr 14, 2017 · FAQ: Asymptote of a curve in polar coordinates What is the definition of an asymptote in polar coordinates? In polar coordinates, an asymptote is a straight line that the curve approaches but never touches, as the distance between the curve and the line approaches zero as the distance from the origin increases.
Vertical Asymptote: Is f Defined at x=1? - Physics Forums
May 22, 2011. Asymptote Vertical. In summary, the statement "If the line x=1 is a vertical asymptote of y = f (x), then f is not defined at 1" is false. A counterexample is given by the function f (x) = 1/ (x-1) - 1, where f (1) is defined as 5. This shows that a function can still be defined at a point where there is an asymptote, but under ...
Determining the horizontal asymptote - Physics Forums
Apr 9, 2024 · 22,155. 13,701. An asymptote is about how a curve behaves at infinity, not how the behaviour looks in some intermediate range. It does not matter at all if it crosses the curve or not. All that is relevant is whether or not the curve approaches the asymptote at infinity. chwala said:
Cubic/cubic ->intercepts and asymptote(s) - Physics Forums
Mar 29, 2011 · I was taught that a horizontal asymptote is an end behavior asymptote - the graph of a function with a horizontal asymptote will approach some y-value at the "ends" of the graph. (Now, some graphs will have a horizontal asymptote when you look at one "end" of the graph but not at the other "end" -- look at exponential functions, for instance.)