Math Rational Functions-Please Clarify =)
posted by Enlia .
I have a question about the rational function I recently posted. Would the range still be (-∞,2)U(2,∞) if the rational function is what Reiny posted "(2x^2-18)/(x^2+3x-10)." The y-intercept confuses me because its (0,1.8) and when I look at the line it passes through the horizontal asymptote.
Here is a wonderful webpage that let's your graph just about any curve
enter your function with brackets in the form
set: "range x-axis from" -20 to 20
set: "range y-axis from" -20 to 20
you will see your y-intercept correct at (0,1.8)
and the two vertical asymptotes of x = -5 and x = 2
starting to show.
Horizontal asymtotes begin to show up only when x approaches ± infinity, so if you look to the far right, the curve approaches y = 2 from the bottom up, and if you look far to the left, the curve approaches y - 2 from the top down
It is very common for the curve to intersect the horizontal asymptote for reasonable small values of x.
If we set our function equal to 2,
(2x^2-18)/(x^2+3x-10) = 2 , and cross-multiply we get
2x^2 - 18x = 2x^2 + 6x - 20
x = 20/24 = 5/6 , which is shown on the graph
But as x --> ±∞ , the function will never again reach the value of 2
(try it on your calculator, set x = 500 and evaluate
then let x = -500 and evaluate,
in the first case you should get 1.988... a bit below 2
in the 2nd case you should get 2.012... a bit above 2
the larger you make your x, the closer you will get to 2, but you will never reach it, and that is your concept of an asympote )
Thank you very much!
you are welcome,
does it make sense now?
Yes it does ^^