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a selection of answers from the Dr. Math archives.
- Etymology of 'Asymptote'
- Where does the term 'asymptote' come from?
- When do asymptotes occur?
- Vertical and Horizontal Asymptotes
- What are the vertical and horizontal asymptotes?
- Graphing a Function with
- 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)/(3-6x) 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
- 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/(x-3).
- Oblique Asymptote
- I have a question about the oblique asymptote of the function:
- Nonvertical Asymptotes
- Does this problem have slant asymptotes?
- Line Crossing Horizontal and
- For the function y = (5x+1)/(x^2-1), why does the line between its
two vertical asymptotes and one horizontal asymptote cross?
- Rational Function
- Given the rational function y=r(x)=(4x^6-x^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)^2-4 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^4-4x^3-12x^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 (x-4)/x^2
- For the function (x-4)/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?
High School Equations/Graphs/Translations
Index of Selected Answers to Common Questions
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