ExpGraphing

# ExpGraphing - Sample Graph Sketching Problem Let's do a...

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Sample Graph Sketching Problem 1 Let's do a graph sketching problem. We'll look at the graph of the function: ( ) It's probably easier to find what isn't in the domain. Functions like are continuous on all x x y e f x e = = Step #1: Domain { } 1 . The only possible problem here is with . This function is undefined at 0, so our composite function will also be undefined at 0. Our domain then is: 0 , or in other words, all such t x x x x x x x = = ( 29 ( 29 1 1 ( ) hat ,0 0, Let's check the usual suspects. 1) : Does ( ) ( ) for some real -value? 2) / : We look at ( ) , x x x Periodic f x f x a a NO Even Odd f x e e - - - ∞ = + - = = Step #2: Symmetry 1 1 ( ) ( ), so not odd ( ), so not even In all, no usable symmetries. Only bother with these i x x f x e f x e f x - - - = - Step #3: Intercepts 1 f they are reasonably easy to calculate. Here, they are especially easy: 0 isn't in the domain, so no intercept here. 0 , that never happens. Real exponential x x y e = = = : : y - intercept x - intercept 1 1 1 1 0 0 s are > 0. Notice: lim

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ExpGraphing - Sample Graph Sketching Problem Let's do a...

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