1. a) b) c) d) e) f )
9 x
⫺
3 y
⫹
17
4 m
⫹
7 n
⫺
15
⫺
28 a
⫹
4
16 y
⫺
6
⫺
15 m
⫺
13 n
⫺
11
12 a
⫹
14 b
⫹
29
2. a) b) c) d) e)
3 x
2 ⫺
23
15 x
⫺
5 y x
⫺
2 a
⫹
16 m
2 ⫺
22 mn
23
4 a
⫺
8
5 b f )
⫺
9
10 x
⫺
14
15 y
⫹
11
3. a) 2 x
⫺
6 y ; 5 x
⫹
7 y ; the two expression are not b) equivalent
6 a
⫺
4 b ; 6 a
⫺
4 b ; the two expressions are equivalent
4.
If you notice that two functions are equivalent at one value of a variable, it does not necessarily mean they are equivalent at all values of the variable. Evaluating both functions at a single value is sufficient to demonstrate non equivalence, but it is not enough to demonstrate equivalence. Tony evaluated the equations at one point, found the values to be equal, and concluded equivalence of the two functions. If any other point is checked, it can be seen that the two functions are not equal at such points. Thus, the two functions are not equivalent.
5. a) 14;
⫺
14
37 b) , c)
2
⫺
5 ,
⫺
155 d) 200,
2
⫺
18
⫺
202
6. 1) Substitute the same value into each function. If the results are not equal, the two functions are not equivalent.
2) Simplify the functions and compare.
7. a) equivalent b) not equivalent c) not equivalent d) equivalent
388
Functions 11: Lesson 2.1 Extra Practice Answers