The figure illustrates the apparatus for a tightrope walker. two poles are set y = 50 feet apart, but the point of attachment p for the rope is yet to be determined. (a) express the length l of the rope as a function of the distance x from p to the ground.

Since L is to the second pole, not x, we can't simply say that x^2+y^2=l^2 using the Pythagorean Theorem. We can, however, say that (x-2)^2+y^2=L^2 due to that we simply increase the original height by 2, decreasing x by 2. Plugging 50 as y in, we get (x-2)^2+50^2 =L^2. Square rooting both sides, we get L=sqrt((x-2)^2+50^) and therefore a function of x

Check the picture below.