The graph of the function y=f(x) is stretched horizontally by a factor of 1/2 and stretched vertically by a factor of 4. Then, it is reflected in the x-axis and translated 3 units left. The equation of the transformed function can be written as

To determine the number of deer in a forest a forest ranger tags 280 and releases them back

Find the constant of variation for the relation and use it to write an equation for the statement. then solve the equation.

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) = .