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JohnnyPhysics
I the curve (1-2x)/(3x+5). I have been asked to find the verticle and horizontal asymptotes. Can anyone help me with a strategy?
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I don't know but that answer looks a little too complicated...horizontal asymptote: take limit of f(x) as x tends to infinity. What is the relation between the limit value you find and the horizontal asymptote?
Originally posted by FZ+
I don't know but that answer looks a little too complicated...
y = (1-2x)/(3x+5)
3xy + 5y = 1 - 2x
x = (1 - 5y )/(3y + 2)
Now, find the value y can't have...
but beware, I have been wrong before (intentionally of course! )
An asymptote is a line that a curve approaches but never touches. It can be horizontal, vertical, or oblique.
To find the vertical asymptote of a rational function, set the denominator equal to zero and solve for x. The resulting value(s) will be the x-coordinate(s) of the vertical asymptote.
The horizontal asymptote represents the value that the function approaches as the input (x) gets larger and larger. It is also used to determine the end behavior of a function.
To graph a rational function with a slant asymptote, first find the quotient using long division or synthetic division. The resulting quotient will be a polynomial function, which can be graphed as a slant asymptote. Then, plot the vertical and horizontal asymptotes and the points where the function intersects them. Finally, connect the points on the graph to create a curve that approaches the slant asymptote.
Yes, a function can have multiple asymptotes. It can have both vertical and horizontal asymptotes, as well as oblique asymptotes. These asymptotes can intersect or be parallel to each other.