Arledge, 2014
                                                           M408N
             Precalc review: exponential, and log (and some trig and rational) functions
            (1) Simplify the following.
                       2n 3n−1
                 (a) x x
                         n+2
                        x
                      p √
                        a b
                 (b)   √
                        3 ab
            (2) Sketch graphs of the following, without using a calculator. Label all important features, including
                 asymptotes.
                             x
                 (a) y = 10
                 (b) y = 1+cos(x)
                  (c) y =  −x        x<0
                              x
                             e −1 x≥0
                 (d)     x+1
                       2
                      x −2x−3
            (3) Find the domain of the following.
                             √       t
                 (a) h(x) =     1−2
                 (b) g(x) = 1+x
                              ecosx
                  (c) ln(sinx) on the interval [0,2π]
                                     2
                                    x
                 (d) f(x) = 1−e 2
                                   1−x
                              1−e
            (4) Evaluate the following without a calculator.
                 (a) sin−17π

                             6
                 (b) tan(4π)
                           3
                  (c) log ( 1 )
                         3 27
                 (d) e−2ln5
                                           π         √
            (5) Show that ln(2)+ln(sin(3)) = ln( 3)
            (6) Find the exact value(x) of x in the following.
                 (a) e2x −3ex +2 = 0
                 (b) lnx+ln(x+1)=1
                  (c) ln(lnx) = 1