Chapter 9 Radical Functions

SSM: Intermediate Algebra
Chapter 9 Test
18. y = − 2 x + 3 + 1
x y
−3 1
−2 −1
1 −3
6 −5
13 −7
−4
4
−4
y
4
19. a. We need a < 0 and k ≥ 0 , or we need
a > 0 and k ≤ 0 . In either case, h can be
any real number.
b. f ( x)
= a x − h + k
a x − h + k = 0
a x − h = −k
( x h )
k
x − h = −
a
2 ⎛ k ⎞
− = ⎜ − ⎟
⎝ a ⎠
k
x − h =
a
k
x = h +
2
a
⎛
2
k
The x-intercept is h ,0 ⎞
⎜
+
2 a ⎟
.
⎝ ⎠
2
2
x
2
2
20.
21.
22.
2 x + 3 = 13
2 x = 10
x = 5
( ) 2 2
x = 5
x = 25
Check x = 25
( )
2 25 + 3=
13
13 = 13 true
The solution is 25.
3 5x
− 4 = 27
( ) 2 2
5x
− 4 = 9
?
5x
− 4 = 9
5x
− 4 = 81
5x
= 85
x = 17
Check x = 17
( )
3 5 17 − 4 = 27
27 = 27 true
The solution is 17.
3 − 2 x + 9 − x = 0
?
9 − x = 2 x − 3
( 9 − x ) = ( 2 x − 3)
2 2
( 12 x ) = ( 5x)
2
( x )
9 − x = 4x − 12 x + 9
12 x = 5x
2 2
144x
= 25x
25x
− 144x
= 0
x 25 − 144 = 0
x = 0 or 25x
− 144 = 0
144
x = 0 or x =
25
Check x = 0
( ) ( ) ?
3 − 2 0 + 9− 0 = 0
Check
144
x =
25
?
2
6=
0 false
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