Answer Key 235

5. −=

−

−

1

3

2

y

x

−1(x − 2) = y − 3

−x + 2 = y − 3

y = −x + 5

6.^1
5

=y−^1

x

x = 5y − 5

5 y=x+ 5

yx=+x

1

5

1

7. y
   x

−

−

(^4) =
2
42 −
21 −
y
x
−
−

4
2
2
y − 4 = 2(x − 2)
y − 4 = 2 x − 4
y= 2 x
8.
y
x
−
−

−

2
1
22 −
11 −
0
y − 2 = 0
y= 2
9.
y
x
−
= =−
11 −
21 −
1
y −1 = − x
y= −x + 1

10.^64
64

4

4

= −

−

y

x

1

4

4

=

−

−

y

x

y − 4 =x − 4

y= x

Chapter 19 Basic Function Concepts

Exercise 19

1. a. f = {(2, 1), (4, 5), (6, 9), (5, 9)}
   b. g = {(3, 4), (5, 1), (6, 3), (3, 6)}
   c. h = {(2, 1)}
   d. t = {(7, 5), (8, 9), (8, 9)}
   Only f, h, and t are functions. Note that in t, (8, 9) and (8, 9) are the same point.


2. The domain is {4, 6, 7, 8} and the range is {5, 7, 9}.


3. a. y = f(x) = 5 x − 7 The domain is the set of all real numbers.

b. yg()x 23 xxx− + 4

Set 2x − 3 ≥ 0 and solve.

2 x − 3 ≥ 0

2 x ≥ 3

x≥

3

2

. The domain is the set of all real numbers greater than or equal to

3

2

.