Math Is Fun Forum

amnkb wrote:

"odd" means it matches on both sides of diagonal y = x

**

That's not the definition I have always used.

https://www.mathsisfun.com/algebra/func … -even.html

The url in post 3 worked when I made my post but not now.  Maybe the poster removed it from imgur ???

There were two graphs. The first was y = x^2 or something similar. The second was, I think, y = e^x or some thing similar. There were no scales so the exact function could not be determined but enough to show the symmetry or not.

Bob

ps ** If a graph of a function is reflected in the line y=x this is equivalent to interchanging y and x and the resulting graph shows the inverse function.

eg.  Compare y = 2x + 3 and y = (x-3)/2

A function is said to be even if it is symmetrical in the y axis.  Here are some examples:

y = x^2

y = x^4

y = x^6 + x^4 - x^2

From these examples you can probably see why these are called even functions.

To test algebraically replace every x in the function with -x.  If you get the same function back, then it's even.

example:

y = x^2 Replace x with -x  .... ynew = (-x)^2 = x^2 = y. So y is even.

In a similar way odd functions have rotational symmetry around the origin order 2. ie. If you rotate the graph 180 around (0,0) and the graph looks the same then it is a odd function.

example:

y = x^3

But most likely, a function is neither The second example looks like y = e^x and this is neither odd nor even.

If you track left on the graph, as x tends to minus infinity y tends to zero. There are no negative y values. As you track right, as x tends to + infinity y tends to + infinity.  So the range is (0, + infinity). The round brackets indicate that the endpoints are never achieved.

Bob

Note that

The two expressions have p^2 in it and 2ap if you put a = 7

So add a^2 = 49 and you have a perfect square.

As a general rule find half the middle coefficient (14/2 = 7) and square it (49).

Bob

harpazo1965 wrote:

I am thinking of a number. It lies between 1 and 10; it's square is rational and also lies between 1 and 10. The number is larger than pi. Correct to 2 decimal places (that is, truncated to two decimal places) name the number.

ne # between these works

infinitely many others do 2

harpazo1965 wrote:

Suppose that m and n are positive integers with m > n.
If a = (m^2 - n^2), b = 2mn, and c = (m^2 + n^2), show that a, b, and c are the lengths of the sides of a right triangle. 

Note: This formula can be used to find the sides of a right triangle that are integers such as 3, 4, 5; 5, 12, 13; and so on. Such triplets of integers are called Pythagorean triplets.

NOTE: Looking for the set up only.

I suspect that they're expecting you to notice how the given side-length expressions hint of connections to perfect-square trinomiais.

If you add two of the above expressions, you get the third of the above expressions. Which pair works?

You need to show that two of these when squared and added make the same result as the third when squared.

But which to choose? I can see that c is bigger than a.  So I suggest working out c^2 and write that down. Then get an expression for a^2 + b^2. If this comes to the same as c^2 then you are done.

Bob