Is the graph of the function f(x) = 4/x, symettric over the x-axis, the y-axis, the origin, or not symettric?

Answer 1

It is symmetric across the origin.

That is, f(x) = -f(-x).
4/x = -4/(-x)

Answer 2

x can not be zero, since one can not divide by zero.

for other values

x = -1000; y is almost zero
x = - 8; y = -1/2
x = -4; y = -1
x = -1/4; y = -16
x = -1/1,000; y = -4,000
x = 1/1,000; y = 4,000
x = 1/4; y = 16
x = 4; y = 1
x = 8; y = 1/2
x = 1,000; y is almost zero

This should form two curved lines. The shapes represent boomerangs. One faced up and to the right. The other faces down and to the right.

For positive numbers, as x approaches zero, y will be negative infinity. As x approaches positive infinity, y will be close to zero.

For negative numbers, as x approaches zero, y will be positive infinity. As x approaches negative infinity, y will be close to zero.

Again there is no value for x = 0.

Answer 3

y = 4/x has symmetry about the origin and the line of y = x
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Ideas: 4/(-x) = - 4/x and xy = yx = 4

Answer 4

uhh false?