Please graph the function Y=Tan X. Asymptotes will be used! (Probably only Frank Sanoica and Faye Fox will be able to draw the graph) Hal

Why, out of curiosity do you need the graph? Asymptotes occur at every odd integral multiple of pi/2 Any trig student should know that.

Yes, Hugh...I've always thought that any asymptote has that "magical" quality of being "untouchable" no matter how close a curve gets to it! It's just one of those unbreakable rules in Mathematics, such as dividing by Zero...It's undefined! Hal (Algebra, Geometry, and Trig in High School...Calculus in College.)

Here's a math puzzle: Under what conditions do the numbers 1, 10, 100, and 1000 have the same numerical value? (I made this one up myself)

Even more interesting: Y = arc Tan X Also asymptotic, it's theorized the extreme y-values meet at X = infinity. Worse, how about a matrix of numbers, like: These are quite valuable at solving linear equations such as: x + 2y = 10 3x - 7y= 17 -2x + y = 28 Other means are available, such as "substitution". However, in Linear Algebra, I was hit with matrices having numbers of columns and rows approaching infinity! My worst of all Math courses. Frank

To respond to Al 's comment, I realize that asymptotes are just dust under the rug for most of us, but I happen to find mathematical oddities fascinating as to what they represent in the real world! For example, the simple, innocent expression Y=X/0 represents a number so great as to be unimaginable, and this I find very interesting! Also, the expression "Parallel lines meet at infinity" is just as correct as saying they "never meet", which is how most of us see it. H.P.

Frank's set of equations can't be solved: x + 2y = 10 3x - 7y= 17 -2x + y = 28 You have more equations than variables. For example x =8, y=1 would solve the first 2, but would yield -15 = 28 in the third, so clearly, no solution.

No, its just fun to do math. Also, you can have asymptotes that are not vertical, such as this: the graph of y = (x^2 +1)/(x - 1) or alternately y = x + (x + 1)/(x - 1) , so we can see that there is an oblique asymptote.