Math Is Fun Forum

Enshrouded_

Member

Registered: 2015-07-31

Posts: 47

Asymptotes

A function

has horizontal asymptote of

a vertical asymptote of

and an

-intercept at

Part (a): Let

be of the form

Find an expression for

Part (b): Let

be of the form

Find an expression for

Please don't just give an answer, if you can, please explain.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Asymptotes

hi Enshrouded_

part a:

For a vertical asymptote the curve will become more and more vertical as x approaches the key value; in this case 3.

To make that happen set x + c = 0.   Then as x approaches 3, x + c approaches zero and division by zero results in an infinite answer.  So 3 + c = 0

For a horizontal asymptote, you want the function to tend to a fixed value as x approaches + or - infinity.

When f(x) = (ax+b)/(x+c) and x is approaching infinity the b and c values are insignificant and the function is the same as f(x) = (ax)/x = a

So a horizontal asymptote of y = -4 means we want a = -4

To find 'b', use the known point on the curve.

When you have an answer you can try it out at http://www.mathsisfun.com/data/function-grapher-old.php

part b.

When x = 3 you want 2x+t to be zero.

As x tends to infinity the function behaves like r/2 which will fix r.  And finally find s by using the known point.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Enshrouded_

Member

Registered: 2015-07-31

Posts: 47

Re: Asymptotes

I don't get how you did the as x approaches 3 you get an infinite answer. Thanks.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Asymptotes

What I'm looking for is a denominator that is zero at x=3

So x + c = 0 => c = -3

Here is a demo with 1/(x-3)

You can see that as x gets closer to 3 from below or above, the value of the expression gets bigger and bigger.  If you plot the points the curve becomes more and more vertical as you get closer to x = 3

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob