 Asymptotes,
a selection of answers from the Dr. Math archives.
 Etymology of 'Asymptote'
 Where does the term 'asymptote' come from?
 Asymptotes
 When do asymptotes occur?
 Vertical and Horizontal Asymptotes
 What are the vertical and horizontal asymptotes?
 Graphing a Function with
Asymptotes
 How do you find the asymptotes of f(x) = (2x + 1)/(x  3)?
How do you use the asymptotes to graph the function?
 Finding Asymptotes
 In the equation y = (m/x) + c, how do the values of m and c
affect the graph? How do you find the asymptotes?
 Domain, Range, and Asymptote
 How do you find the domain, range, and asymptote of a function?
 Asymptote of a Function
 Determine the value of A so that y = (Ax+5)/(36x) has a horizontal
asymptote at y = 2/3.
 Testing for Horizontal Asymptotes
 Is there a rule for testing whether or not an equation has a horizontal
asymptote?
 Finding a Vertical Asymptote
 Find the vertical asymptote of the equation xy^2  x^3y = 6.
 Domain, Asymptotes, Intercepts
of a Function
 What is the domain of this function? What asymptotes does it have?
What are the x and y intercepts? Etc...
 Oblique Asymptotes
 I'm stuck on how to calculate oblique limits, for example, x^2/(x3).
 Oblique Asymptote
 I have a question about the oblique asymptote of the function:
F(X)=(X^33X^2+2X8)/(X^2+4X+4)...
 Nonvertical Asymptotes
 Does this problem have slant asymptotes?
 Line Crossing Horizontal and
Vertical Asymptotes
 For the function y = (5x+1)/(x^21), why does the line between its
two vertical asymptotes and one horizontal asymptote cross?
 Rational Function
 Given the rational function y=r(x)=(4x^6x^4)/(x^5+5)
describe its end behavior and find all vertical and horizontal
asymptotes for r if they exist.
 Similar Graphs
 How would you describe how the two graphs of y = 1/sqrt(x)^2
and y = 1/sqrt(x)^24 are similar and dissimilar?
 Trigonometric Functions and
the Unit Circle
 Why don't sine and cosine graphs have values greater than 1 or less
than 1? Why does the tangent graph have asymptotes? How do the trig
functions relate to the unit circle?
 Analyzing a Function
 Find the domain, intercepts, asymptotes, critical points, points of
inflection, and graph of the function: y = 3x^44x^312x^2.
 Dominant Terms
 What are dominant terms, and how do you obtain their values?
 Focus of a Hyperbola
 When you rotate the focus point of a hyperbola around the center,
why does it hit the asymptote with the same x coordinate as the vertex?
 X = TanX
 Show that x = tanx has an infinite number of solutions.
 Asymptote for (x4)/x^2
 For the function (x4)/x^2 there is a horizontal asymptote at y=0;
however, at x=4 y=0 the graph of the function does intersect the line
that is supposed to be the asymptote. How can this be if by definition
the asymptote is a line that the function gets close to but does not touch?
