BMQ Solutions to Tutorial 4 (RVHS)

H2 Mathematics (9758) JC 1 River Valley High School, Mathematics Department, 2022 BMQ Solutions to Tutorial 4: Functions Basic Mastery Questions 1. State, with reasons, which of the following relationships are functions. (a) Because 1 ↦ 5 and 1 ↦ 2 1 has no unique image. Therefore this is not a function. (b) Every element in the domain has exactly one image in the range. Therefore this is a function. Note: Many -One relationships are still functions (c) A vertical line intersects the curve at 2 separate points. Therefore, it is a one-many relationship Therefore it is not a function. (d) The relationship maps a number to all real numbers. Therefore, it is a one-many relationship Therefore it is not a function. (e) y = 2 y = 2 is a function, since any , 2xx . Therefore each element has exactly one image Therefore it is a function. 1 2 3 5 2 7 10 3.1 11 -2 20.1 3

H2 Mathematics (9758) JC 1 River Valley High School, Mathematics Department, 2022 (f) yx yx is not a function since any x > 0 is mapped to 2 values. Alternatively, this graph fails the vertical line test. 2. State the range of the following functions. (a) 2f : 2 ,x x x x  From the graph,  1,fR    (b) 2 1f : , 1xx x  From the graph,  0,1fR  (c) 2g : , 1 1 1 xxx x   - From the graph,  ,0fR   (d) 32g : 5 4 , (0,4)x x x x x   From the graph (and using GC),  6.06,0.879fR  3. State, with reasons, whether the following functions have an inverse. (a) 1f : , 0xx x  

H2 Mathematics (9758) JC 1 River Valley High School, Mathematics Department, 2022

H2 Mathematics (9758) JC 1 River Valley High School, Mathematics Department, 2022 (b) 2g : 2 , 0x x x x  (c) 2h : 2 , 2x x x x   (d) h : ln 2 , 0x x x

H2 Mathematics (9758) JC 1 River Valley High School, Mathematics Department, 2022 4. State, with reasons, whether the composition gf exists for the following functions.