Statement :

All tangents to the graph of pass through the origin.

From the statement the graph is symmetric about the axis and also has a tangent line with a slope of or .

.

Where .

If , then and If , then and is a tangent line at any point on the graph and is on the tangent line.

Therefore, the tangent line passes through the origin.

If , then and If then .

If , then .

But is the tangent line and is on the tangent line.

If , then .

The function is .