30 points! Using an example explain what the graph of a rational function looks like. Contrast this with other functions we have studied. (Linear, quadratic etc.)

Divide the following fractions 3/4 ÷ 2/3 1/2 8/9 9/8 2

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) = .

Micheal is 4 times as old as brandon and is also 27 years older than brandon. how old is micheal