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davidtrinh

Member

Registered: 2016-12-03

Posts: 10

How to distinguish between these two graphs?

Consider the two functions f(x) = x^2 and g(x) = 1/|x|.

The first one is a parabola with the vertex at the origin. The second one is an absolute value function with a V-shaped graph.

If you take the reciprocal of both functions, their graphs look very similar.
Both have an asymptote along each axis and their curves are in quadrants one and two.

If you just see their reciprocal graphs, how can you tell which graph is represented by which reciprocal function?

Can someone explain this? Thanks a lot.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: How to distinguish between these two graphs?

Hi;

You will not always be able to figure which function goes with which graph just by visual inspection.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: How to distinguish between these two graphs?

hi davidtrinh

If you use the MathIsFun function plotter then you get colour coded graphs, so it's easy.

But, more seriously, you can analyse their behaviour by considering what happens as x approaches zero.

X^2 gets smaller at a rate dependent on the square function; x just gets smaller at a linear rate.  So the first gets smaller more quickly.  This effect reverses when you take the reciprocal; 1/x^2 gets larger more quickly.

You can also test this by considering a value.

Take x = 0.5.  1/x = 2    1/x^2 = 4 so the blue graph is higher at x = 0.5

Try x = 0.1     1/x = 10   1/x^2 = 100  the blue graph is now much higher.

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

davidtrinh

Member

Registered: 2016-12-03

Posts: 10

Re: How to distinguish between these two graphs?

Thank you very much, bob bundy.