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Show whether the set of ordered pairs (x,y) below defined by each equation is a function.

(a) y = x^3 - 3x

(b) x + 2y^2 = 1

2007-06-15 12:51:17 · 3 answers · asked by planetmath 1 in Science & Mathematics Mathematics

3 answers

for something to be a function that means that for any x that you plug in, you have to get just one y. If you get several possibilities for y, then it's not a function. So, a is nice because it's already solved for y and you can see that for any value of x, there will be just one y.

If we slove b for y, we will get y = + or - squareroot( (1-x)/2). Because it's plus or minus. That means that for any x value other than 0, we'll get two answers and therefore it's not a function.

2007-06-15 13:02:24 · answer #1 · answered by Ace 1 · 0 0

clearing in a), for any given x there's only 1 y.

but in b, solving for y, we get

2y² = 1 - x
y² = 1/2 - x/2
y = ±√(1/2 - x/2)

and that's 2 values of y for any given x (in the domain).

2007-06-15 13:02:51 · answer #2 · answered by Philo 7 · 0 0

a) since it's a cubic, it's a function
b) since it's a parabola ( x = type), it's not a function.

2007-06-15 13:06:02 · answer #3 · answered by richardwptljc 6 · 0 0

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