i need help on this math problem. I don't know why x^2+y^2=9 isn't a function.
2006-09-12 04:55:28 · 12 answers · asked by comakazi l 2 in Science & Mathematics ➔ Mathematics
Graph the equation, then use a "special" type of test to figure this out.
2006-09-12 04:57:38 · answer #1 · answered by raz 5 · 0⤊ 0⤋
Let's have a summary of Sets, Relations and Functions.
Relation: It is a mapping that connects two given sets(that is, variables in the two sets; the set from which the variable was taken as INPUT is the domain and the set,whose variable was OUTPUT is co-domain.)(Input is x and output is y.)
Function: It is a special type of relation which has following condns:
(1) Every element of the domain has to be taken for INPUT;
(2) Every element of the domain MUST have a UNIQUE OUTPUT.
Now, you can see that :
x^2 + y^2 = 9 is a relation as it connects two variables(x and y). But; it is not a function as for each x, it has two corresponding values of y. EX: If x = 1, y = +/- root(8)
Note:
It can be checked very easily by graph. If a line parallel to Y-AXIS cuts the graph of a relation two times, then it is not a function. And as the graph is circular, it is evident.
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2006-09-12 13:09:26 · answer #2 · answered by An Indian guy 2 · 0⤊ 0⤋
Mathematics a function. A variable so related to another that for each value assumed by one there is a value determined for the other.
The formula is either an ellipse or a circle. For every value of x, there is two values for Y and the reverse is true. If there was one value for Y for every X, it would be a function
2006-09-12 12:04:25 · answer #3 · answered by Mr Cellophane 6 · 0⤊ 0⤋
By definition of a function, each possible value of x can only have one value of y that works. Here, if x = 0, y could be 3 or it could also be -3. So it isn't a function.
2006-09-12 12:02:08 · answer #4 · answered by hayharbr 7 · 2⤊ 0⤋
Any equation with a y^2 is not a function because you have two values for y for each value of x - contradicts the definition.
2006-09-12 13:45:37 · answer #5 · answered by MollyMAM 6 · 0⤊ 0⤋
if we express y in terms of x
y^2=9-x^2
y=(9-x^2)^1/2
for values of x <=3 for each value there will be two values of y
which goes against the definition of a function and so it is not a function
2006-09-12 11:59:24 · answer #6 · answered by raj 7 · 2⤊ 0⤋
Because it has multiple Y values at a given X value. Functions can only have 1 Y value for a given X value.
2006-09-12 12:01:19 · answer #7 · answered by Anonymous · 0⤊ 0⤋
It's the equation of a circle and has more than one y value for each x value
2006-09-12 12:09:23 · answer #8 · answered by Anonymous · 0⤊ 0⤋
that is a funtion!!!!
a function for a circle.
it mighten be a straight line or polynomial
this i think is called an implicit function.!!!!
2006-09-12 18:06:57 · answer #9 · answered by Anonymous · 0⤊ 0⤋
It is a polynomial with two variables.
2006-09-12 11:59:53 · answer #10 · answered by openpsychy 6 · 0⤊ 0⤋