Math Is Fun Forum

Alive

Member

Registered: 2010-08-14

Posts: 92

Need the asymptopes Of these graphs (100% Understandable Pictures)

How do we find the equations of asymptotes of these?

a)

b)

c)

d)

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All things can be forgiven if we can progress.
Yusuf Islam (formerly known as Cat Stevens)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Need the asymptopes Of these graphs (100% Understandable Pictures)

Hi Alice,

An asymptote is a straight line that the curve approaches (tends to) without ever meeting (and therefore crossing).

(a)  As you track towards the right along this curve it just carries on getting higher and higher without limit so no asymptote there.
But, as you track left the curve gets flater and flater; 2^x tends to zero as x tends to minus infinity; so the asymptote is Y = -4

(b)  Interesting the way your graph software has handled negative x values; normally I wouldn't expect to see any curve left of the y axis for no real log values exist there. [You may not have met 'complex' numbers yet, in which case don't worry.]

Again, there's no asymptote to the right as log curves just carry on getting bigger, but much more slowly than exponentials (a).
As x tends to zero, y tends to minus infinity, so the asymptote is the y axis itself.

(c) and (d) are similar but the asymptote is translated 4 units right.  Don't be put off by the apparent flattening out of these curves for large positive or negative x.  It might look as though the curves will eventually level off but they don't.  If you can alter the x scale to show much higher values of x, you'll see that the curve in (d) crosses the x axis eventually and goes on getting bigger and bigger.

Bob

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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

Alive

Member

Registered: 2010-08-14

Posts: 92

Re: Need the asymptopes Of these graphs (100% Understandable Pictures)

Maths is fun thanks to you guys

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All things can be forgiven if we can progress.
Yusuf Islam (formerly known as Cat Stevens)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Need the asymptopes Of these graphs (100% Understandable Pictures)

Hi Alive,

You're welcome.  Whoops I seem to have called you Alice earlier.  Apologies.

B

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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