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2
FUNCTIONS
2.1
FUNCTIONS
1. If f x x 3 1, then (a) the value of f at x (b) the value of f at x
1 is f
13
1 23
2 is f 2
1
1
0.
9.
(c) the net change in the value of f between x
1 and x
2 is f 2
f
1
9
0
9.
2. For a function f , the set of all possible inputs is called the domain of f , and the set of all possible outputs is called the range of f . x 5 3. (a) f x x 2 3x and g x have 5 in their domain because they are defined when x 5. However, x h x
x
(b) f 5
52
10 is undefined when x 3 5
25
15
5 because 5
10 and g 5
5
5 5
10
5, so 5 is not in the domain of h.
0 5
0.
4. (a) Verbal: “Subtract 4, then square and add 3.� (b) Numerical: x
f x
0
19
2
7
4
3
6
7
5. A function f is a rule that assigns to each element x in a set A exactly one element called f x in a set B. Table (i) defines y as a function of x , but table (ii) does not, because f 1 is not uniquely defined. 6. (a) Yes, it is possible that f 1
f 2
(b) No, it is not possible to have f 1 value of f x .
5. [For instance, let f x 5 and f 1
5 for all x .]
6. A function assigns each value of x in its domain exactly one
7. Multiplying x by 3 gives 3x , then subtracting 5 gives f x
3x
5.