Math Is Fun Forum

nycguitarguy

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 571

Reciprocal Function Properties

Let f(x) = 1/x be the reciprocal function.

1. Why is the domain and range of this function the set of all nonzero real numbers?

2. Why is this function odd?

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The Rapture is the central event in biblical prophecy. The greatest truth about the Rapture is not its timing but it's reality. The Rapture will be the great disappearance.

Dr. David Jeremiah

Bob

Administrator

Registered: 2010-06-20

Posts: 10,214

Re: Reciprocal Function Properties

Arhhh! Here is the function y = 1/x. Looks like you got this and the previous question muddled.

Using graph sketching techniques:

When x tends to - infinity y tends to zero from negative values.

When x tends to infinity y tend to zero from positive values.

As x approaches zero y tends to infinity when x>0 and - infinity when x<0

So the graph has two elements: from the left starts close to zero and gets more and more negative as x approaches zero from the left.

It is undefined at x = 0. **

After that it 'comes down' from infinity and gradually tends to zero as x gets bigger.

x and y are never zero so are excluded from the domain and range.

(x, 1/x) lies on the graph and so does (-x, -1/x) which means f(-x) = - f(x).

Bob

** My advanced level teacher said the two sections of the graph meet 'round the back of infinity'  !!! This is, of course, complete rubbish; even if you have a smile on your face as you say it.  She wasn't really up to the needed standard for an A level teacher.  She made other errors, one of which helped me to get a place at university! They asked about mathematical induction and I gave her definition. The interviewers looked puzzled and asked if that was what I thought too. I answered "no" and gave the correct definition and explained why I was right and she was wrong.  I learnt much later that my answer was one of the reasons they offered me a place!

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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

nycguitarguy

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 571

Re: Reciprocal Function Properties

Arhhh! Here is the function y = 1/x. Looks like you got this and the previous question muddled.

Using graph sketching techniques:

When x tends to - infinity y tends to zero from negative values.

When x tends to infinity y tend to zero from positive values.

As x approaches zero y tends to infinity when x>0 and - infinity when x<0

So the graph has two elements: from the left starts close to zero and gets more and more negative as x approaches zero from the left.

It is undefined at x = 0. **

After that it 'comes down' from infinity and gradually tends to zero as x gets bigger.

x and y are never zero so are excluded from the domain and range.

(x, 1/x) lies on the graph and so does (-x, -1/x) which means f(-x) = - f(x).

Bob

** My advanced level teacher said the two sections of the graph meet 'round the back of infinity'  !!! This is, of course, complete rubbish; even if you have a smile on your face as you say it.  She wasn't really up to the needed standard for an A level teacher.  She made other errors, one of which helped me to get a place at university! They asked about mathematical induction and I gave her definition. The interviewers looked puzzled and asked if that was what I thought too. I answered "no" and gave the correct definition and explained why I was right and she was wrong.  I learnt much later that my answer was one of the reasons they offered me a place!

Thank you for sharing your story about how you landed the position at the university through someone else's ignorance.

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The Rapture is the central event in biblical prophecy. The greatest truth about the Rapture is not its timing but it's reality. The Rapture will be the great disappearance.

Dr. David Jeremiah