Chapter 9 Radical Functions

SSM: Intermediate Algebra Homework 9.5
65. h( x)
=
x + 1 − 2
x + 1 + 2
x + 1 − 2 x + 1 − 2
= ⋅
x + 1 + 2 x + 1 − 2
=
( x + 1) − 2( x + 1)( 2) + ( 2)
2 2
( x + 1) − ( 2)
x + 1− 4 x + 1 + 4
=
x + 1−
4
x − 4 x + 1 + 5
=
x − 3
2 2
67. a. The square root model would fit best
because it continues to increase slowly. The
quadratic function would reach a peak and then
start to decrease.
79. Answers may vary. The graph of f can be found
by translating the graph of y = a x horizontally
by h units (left if h < 0 and right if h > 0 ), and
vertically by k units (up if k > 0 and down if
k < 0 ).
Homework 9.5
1.
x = 5
( ) 2 2
x = 5
x = 25
Check x = 25
( ) =
?
25 5
5 = 5 true
The solution is 25.
b. S ( 20)
= 3.9 20 + 280 ≈ 297.44
The average test score in 2002 would be
about 297.
c. S ( 23)
= 3.9 23 + 280 ≈ 298.70
The average test score in 2005 would be
about 299.
69. f ( − 6)
= 0
71. f ( 0)
= 2.4
73. x = − 6
75. x = 3
77. ( ) ( )
f x = 2 x + 3 + 2; g x = − 2 x + 3+
2
The graph looks like a parabola that opens to the
right. The relation is not a function because it
would fail the vertical line test.
3.
5.
7.
x = −2
( x ) = ( −2)
2 2
x = 4
Check x = 4
( ) ?
4 =− 2
?
2 =− 2 false
There are no real solutions.
3 x − 1 = 5
3 x = 6
x = 2
( ) 2 2
x = 2
x = 4
Check x = 4
( )
?
3 4 − 1=
5
5 = 5 true
The solution is 4.
4 − 5 x = 2 x −10
− 7 x = −14
x = 2
( ) 2 2
x = 2
x = 4
Check x = 4
289