Rational Functions?

Question

To start with, without using math jargon, what is an asymptote?

Find the vertical, horizontal and oblique asymptote, IF ANY, of each rational function below.

(1) R(x) = (3x + 5)/(x - 6)

(2) F(x) = (-2x^2 + 1)/(2x^3 + 4x^2)

What is the difference between a vertical, horizontal and oblique asymptote, in simple words?

Answer 1

An asymptote is a line towards which the graph of a function tends, but which that graph doesn't intersect. Horizontal ones are horizontal lines, vertical ones vertical lines, and oblique ones lines with slopes that are defined but not zero. Your first example has the vertical asymptote x = 6 and the horizontal asymptote y = 3. Your second example has vertical asymptotes at x = 0 and x = -2, and the x-axis (y = 0) acts as its horizontal asymptote. Neither example has an oblique asymptote.

Answer 2

Factoring the numerator and denominator supplies y = (x-a million)(x² + x + a million) / x(x+2) a) via holes, i assume it potential detachable discontinuities. do no longer see any straight forward aspects so no. b) Vertical Asymptotes at x=0, x=-2 oblique Asymptote: (x-2) (i.e. the quotient of (x³-a million) / (x²+2x) word: A graph won't be able to have the two a horizontal AND oblique asymptote. c) it fairly is on no account achievable for a graph to decrease vertical asymptotes, inspite of the undeniable fact that it would desire to be achievable to circulate over horizontal ones and oblique ones.

Answer 3

asymptote is where the function (the curve) will go to infinity (it wont curve anymore)

verticle is a y value

horzontal is a x value

oblique is the equation of a line

Answer 4

It comes ever closer but does not touch. Here's the dictionary:

"straight line continually approaching but never meeting a curve," 1656, from Gk. asymptotos "not falling together," from a- "not" + syn "with" + ptotos "fallen," verbal adj. from piptein "to fall" (see petition).

Answer 5

the pending

Answer 6

whoa bud too complex