Test 1 solutions

# Test 1 solutions - TEST 1 SOLUTIONS 1.5pts Find the natural...

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1 TEST 1 SOLUTIONS 1.5pts Find the natural domain and range of ( 29 2 3 f x x = - Since 2 3; 3 3 x x or x ≤ - is the domain. Since 2 3 0; y 0 x - is the range. 2.5pts Explain why the function ( 29 ( ( ( 29( 29 2 2 1 2 1 x x f x x x - = - has one or more holes in its graph and a) state the x-values at which those holes occur, The function is not defined if x = -2 or x = 1 b) find a function g whose graph is identical to that of f , but without the holes. ( 29 ( ( ( 29( 29 ( 29( 29( 29 ( 29( 29 2 2 1 2 1 1 1 2 1 2 1 x x x x x f x x x x x x + - + + - = = = + + - + - if we ignore the holes – so ( 1 g x x = + 3.8pts Sketch the graph of 1 2 1 y x = - by translating and reflecting the graph of 1 y x = . Graph intercepts and show any asymptotes as broken lines. Note that the intercepts Are (0, 1) and (-1/2, 0) 4.9pts Let ( ( 3 and 1 f x x g x x = = + . Find the following: a) ( ( ( 2 9 9 3 f g f = = = b) ( ( ( 4 2 9 g f g = = c) ( ( ( 16 4 2 f f f = =

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2 5.5pts Sketch the graph of ( 29 2 2 1 y x = + by making appropriate transformations to the graph of a basic power function. Be sure to graph intercept[s].
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