|Re: TI84 plus really that clumsy??|
Message #10 Posted by Kiyoshi Akima on 6 Sept 2006, 7:03 p.m.,
in response to message #9 by Gerry Schultz
I beg to differ. If I put the -2 inside the parenthesis as "SQ(-2)", I would write that down as (-2)^2, which is 4.
What is confusing me is that when I use the x^2 command, there are no parentheses in the display to clarify what will happen first. For instance, in ALG mode, push x^2 and you get "SQ()", enter -2 and you get 4. If I write that down on a piece of paper, it would be -2^2 which is -4, not 4.
Precedence of operators. ^ has higher precedence than -, just as * has higher precedence than +.
Perhaps the 49g+ is getting around this by using the syntax "SQ()" which would be evaluated as the square of the argument and that will always be positive. If you do -2 y^x 2, the display is -2^2 and you get -4. This means that there are situations where the functions x^2 and y^x give different answers.
In this case, x^2 and y^x are giving different answers because they are given different arguments (actually, the answers are the same, one of them has an additional operator applied after). -2 y^x 2 displays as -2^2 and is interpreted as -(2^2). You don't see the parens but they are there. If you enter (-2) y^x 2, it displays as (-2)^2 and gives 4.
x^2 is indeed a specialized version of y^x. It's the location of the - that's making the difference. Is it negating the 2 before the squaring or is it negating the result of the squaring? In one case you're negating 2 to get -2, then squaring -2 and getting 4. In the other case you're squaring 2 to get 4, then negating the 4 and getting -4.
I think my confusion boils down to this. I always considered the calculator function x^2 and specialized version of the calculator function y^x. What's being said here is that this is not true and here is an example where the two functions evaluate to different answers. That twists my brain but am I correct?
Try evaluating '-3!'. Is that the factorial of -3 or the negative of the factorial of 3? In other symbols, is it -(3!) or (-3)! ? The same principles apply.
Hope that didn't muddy the waters even more.