Drill Practice (1) (2)

SAJC 2020 JC1 H2 Mathematics Lecture Notes Chapter 5: Functions Pa ge 5 of 36 Drill & Practice (1): State the rule, domain and range for each of the given functions: f: 2 1xx 6 , , 1 3xxd d\ f( ) 2 1x x f [1, 3]D >@f 3, 7R 2g: 4 3 ,xx x 6 , 0xx!\ 2g( ) 4 3,xx x g (0, )D f g [1 , )R f p: 2l n ,xx6 1 2, 2xx d\ p( ) 2lnxx @p 1 ,22D § ¨© p (2 l n 2 , 2 l n 2 ]R y x 0 1 7 3 3 y x 0 3 y x 0

SAJC 2020 JC1 H2 Mathematics Lecture Notes Chapter 5: Functions Pa ge 8 of 36 Drill & Practice (2): Determine, with reason, if the following relations are functions. Relation Is fyx a function? Reason 1 , yx x  \ No When ݔൌ 0, ݕis undefined. ݔൌ 0 does not have an image. 1 , yx x  \ Yes Using the vertical line test , this relation is a function because every vertical line ,xk k  \ intersects the curve exactly once. 2 1yx , 1,xxd\ No This relation is not a function since using the vertical line test, x = 0 intersects the graph at more than one point. 1, , 1xxyx  d \ Yes Using the vertical line test , this relation is a function because every vertical line ,, 1xk k k d \ intersects the curve exactly once. 1.3.2 Equivalence of Functions Two functions are the same if and only if they have the same rule and domain. Compare these two functions: 2f: ,xx6 x  \ 2g: x x6 , x \ Although f and g share the same rule, they have different domains. Thus they are different functions altogether. Learning points "