For the proof of Theorem 1.2, toward the end of the proof to show symmetry about the line x = h, the text states:

To show that the graph is symmetric about the line x = h, we need to show that if we move left or right the same distance away from x = h, then we get the same y-value on the graph. Suppose we move ∆x to the right or left of h. The y-values are the function values so we need to show that F(a + ∆x) = F(a − ∆x).

Shouldn't that be that we need to show that F(h + ∆x) = F(h − ∆x)? And shouldn't that follow in the rest of the proof as follows?

Given that

F(h+∆x) = a|h+∆x−h|+k = a|∆x|+k

and

F(h−∆x) = a|h−∆x −h|+k = a|−∆x|+k = a|∆x|+k

we see that F(h + ∆x) = F(h − ∆x). Thus we have shown that the y-values on the graph on either side of

x = h are equal provided we move the same distance away from x = h.

I hope I'm not just overlooking something here. Thanks.

To start a new topic under Stitz Zeager Open Source Mathematics, email

[hidden email]
To unsubscribe from Stitz Zeager Open Source Mathematics,

click here.

NAML