Algebra/Trig Review - Pauls Online Math Notes - Lamar University

Algebra/Trig ReviewAgain, the point of this problem is to make sure you can evaluate these kinds offunctions. Recall that in these problems e is not a variable it is a number! In fact,e = 2.718281828When computing h( x ) make sure that you do the exponentiation BEFOREmultiplying by 5.x = − 2 x = − 1 x = 0 x = 1 x = 2f x 0.135335 0.367879 1 2.718282 7.389056( )g( x ) 7.389056 2.718282 1 0.367879 0.135335h( x ) 5483.166 272.9908 13.59141 0.676676 0.033690x− x5. Sketch the graph of f ( x ) = e and g( x) = e .SolutionAs with the other “sketching” problem there isn’t much to do here other than use thenumbers we found in the previous example to make the sketch. Here it is,Note that from these graphs we can see the following important properties about− xf x = e and g( x) = e .( )xeex−x→∞as x→∞ and e →0 as x→−∞−x→0 as x→∞ and e →∞asx→−∞These properties show up with some regularity in a Calculus course and so should beremembered.x© 2006 Paul Dawkins 84http://tutorial.math.lamar.edu/terms.aspx