According to my analysis, y=f(r) This is an image with an upward groove, but it is not symmetrical. That is, (0, 1 increasing function, 1, the root number 2 is reduced first and then increasing function, the root number 2, the root number 3) subtraction function. When you draw a horizontal straight line with y=k, you can get it by combining numbers and shapes.

As shown below: Without the geometric sketchpad, it is perfect for any teacher to attach an analytical answer, plus a picture.

The explanation is as follows: 1, the root number 2 is reduced first and then increasing function: The whole problem can be understood as the case that a cube intersects a sphere center. When r= 1, f(r)=3 times arc A 1B, when1< r <; When the radical number is 2, f(r)=3 times (arc MN+ arc NQ). In this range, when MNQ is the midpoint of the edge, it is easy to get: arc MN+ arc NQ.

In addition, by the way, give an analytical formula for this paragraph, but this should not be the original intention of the questioner. Make a mountain out of a molehill: f(r)=

，( 1 & lt； R< root number 2)