What do both of these functions have in common?
f(x) = 5ex+5 -5
g(x) = 0.5(x-5)-5
O A. They have the same vertical shift
B. They have the same vertical stretch
O C. They have the same end behavior
O D. They have the same horizontal translation

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .