Properties of Functions & Curve Sketching Domain & Range Questions 1. Write down the largest suitable domain for (a) x x f sin ) ( = (b) 2 ) ( - = x x f (c) ! ) ( x x f = (d) x x f tan ) ( = (e) 2 ) ( x x f = (f) x x f sin 1 ) ( + = (g) 2 ) ( x x f = (h) x x f sin 1 ) ( = 2. State the corresponding range for each of the functions in Q1 where possible. 3. Calculate the range for 6 7 ) ( 2 - + = x x x f Answers 1. (a) x ˛´ (b) 2 x ‡ (c) x W ˛ (d) (2 1) : , where 2 k x x k Z p - ˛´ „ ˛ (e) x ˛´ (f) x ˛´ (g) x ˛´ (h) : , where x x k k Z p ˛´ „ ˛ 2. (a) () [ 1,1] fx ˛- (b) () 0 fx ‡ (c) ( ) (but not all values) fx W ˛ (d) () fx ˛´ (e) () 0 fx ‡ (f) () [0,2] fx ˛ (g) () 0 fx ‡ (h) () 1 or ( ) 1 fx fx ‡ £- 3. 28 () or ( ) 0 25 fx f x £- >
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Properties of Functions & Curve Sketching Domain & Range
Questions
1. Write down the largest suitable domain for
(a) xxf sin)( = (b) 2)( −= xxf (c) !)( xxf = (d) xxf tan)( =
(e) 2)( xxf = (f) xxf sin1)( += (g) 2)( xxf = (h) x
xfsin
1)( =
2. State the corresponding range for each of the functions in Q1 where possible.
3. Calculate the range for
67)( 2 −+
=xx
xf
Answers
1. (a) x ∈ℜ (b) 2x ≥ (c) x W∈
(d) (2 1): , where 2
kx x k Zπ−∈ℜ ≠ ∈
(e) x ∈ℜ (f) x ∈ℜ (g) x ∈ℜ
(h) : , where x x k k Zπ∈ℜ ≠ ∈
2. (a) ( ) [ 1,1]f x ∈ − (b) ( ) 0f x ≥ (c) ( ) (but not all values)f x W∈
(d) ( )f x ∈ℜ (e) ( ) 0f x ≥ (f) ( ) [0,2]f x ∈
(g) ( ) 0f x ≥ (h) ( ) 1 or ( ) 1f x f x≥ ≤ −
3. 28( ) or ( ) 025
f x f x≤ − >
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