Question

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

a. The y-axis
b. The line y = x + 3
c. The point (0,3)
d. The x-axis

Answer 1

c. the point (0,3)

Explanation:

Answer 2

`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).