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

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asked Dec 7, 2019 7.7k views

2 Answers

Techniv · Answer 1 · 2019-12-12T23:28:15+0000

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).