Expand and simplify 1) 3 ( 2x + 1 ) + 5x
2) ( x + 3 ) ( x + 4 )
3) ( x + y ) ^2
4) ( 2x + 1 ) ( x - 3 )

Lassify the function as linear or quadratic and identify the quadratic, linear, and constant terms. f(x) = (3x + 2)(−6x − 3) linear function; linear term: −21x; constant term: −6 linear function; linear term: −18x2; constant term: −6 quadratic function; quadratic term: 6x2; linear term: 24x; constant term: −6 quadratic function; quadratic term: −18x2; linear term: −21x; constant term: −6

Identify the type of observational study described. a statistical analyst obtains data about ankle injuries by examining a hospital's records from the past 3 years. cross-sectional retrospective prospective

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) = .