Catalogue of Important Functions We list several important functions, draw their graphs and indicate domains and ranges. In the forthcoming sections we will study their properties and use them in various applications. As well, we will add more functions t
525-534 Starting with the graph of a known function (see the subsection Catalogue of Important Functions in the previous section) and using transformations, sketch the graph of each function.
525. f (x) = - 526. f (x) =
( x - 3)2
1 x2 1
527. f (x) = x - 7
NEED TO REMEMBER Time: hour (h), minute (min), second (s) Length: metre (m), centimetre (cm), milimetre (mm), foot (ft), inch (in), yard (yd), mile (mile) Mass: kilogram (kg), gram (g), ounce (oz), pound (lb) Time 1 h = 3,600 s = 60 min 1
504-511 Find the formula for the compositions f g and f g . Simplify where possible.
504. f (x) = x 3 , g(x) = 4 - 2x 505. f (x) = 12 - x 2 , g(x) = 4 1 506. f (x) = , g(x) = x - 3 x x -1 1- x 507. f (x) = , g(x) = 2 2 x -1 1 508. f (x) = , g(x) = x +1 x