Question

The equation y=x^3 + 3 is symmetric with respect to which of he following?

Answer 1

$y = x^{3} +3$

Subtract 3 from both sides,

$y-3=x^{3}$

Let x = X and y - 3 = Y

Then,

$Y = X^{3}$

So, we have shifted the origin to a point (0, 3).

This is an odd function and the graph of an odd function is symmetrical about the origin.

That is, symmetrical about X = 0, Y = 0

Symmetrical about x = 0,, y - 3 = 0

Symmetrical about x = 0, y = 3.

Hence, the graph is symmetrical about the point (0, 3).