Chapter 9 Radical Functions

Homework 9.6
SSM: Intermediate Algebra
11. ( 2,6 ) and ( 5,4 )
Substitute the points into the equation
y a x b = + .
6 = a 2 + b
4 = a 5 + b
Rewrite as:
1.4142a
+ b = 6
2.2361a
+ b = 4
Solve the resulting system. Multiply the first
equation by − 1 and add to the second equation.
−1.4142a
− b = −6
2.2361a
+ b = 4
0.8129a
= −2
a ≈ −2.43
2,6 into the equation
Substitute the point ( )
y = − 2.43 x + b and solve for b.
6 = − 2.43 2 + b
b ≈ 9.44
The equation is roughly y = − 2.43 x + 9.44 .
13. Increase the value of b to shift the graph up.
15. a. Start by plotting the data.
( ) = 5.65 t + 10
f t
b. f ( 26) = 5.65 ( 26)
+ 10 ≈ 38.81
c.
In 2008, 38.8% of single-parent fathers will
have never been married.
5.65 t + 10 = 39
5.65 t = 29
( t )
t =
29
5.65
2 ⎛ 29 ⎞
= ⎜
5.65 ⎟
⎝ ⎠
t ≈ 26.35
In 2008, 39% of single-parent fathers will
have never been married.
d. ( 0,10 ) . In 1982, 10% of single-parent
fathers had never been married.
17. a. Start by plotting the data.
2
Answers may vary. A square root model
0,10
may be reasonable. Use the points ( )
and ( 18,34 ) .
Substitute the point ( 0,10 ) into the equation
y = a x + b .
10 = a 0 + b
b = 10
Substitute the point ( )
18,34 into the
equation y = a x + 10 and solve for a.
34 = a 18 + 10
24
a = ≈ 5.66
18
Answers may vary. A square root model
seems to be appropriate. Use the points
52.5,1.94 .
( 0,0 ) and ( )
Substitute the point ( 0,0 ) into the equation
y = a x + b .
0 = a 0 + b
b = 0
52.5,1.94 into the
Substitute the point ( )
equation y = a x and solve for a.
1.94 = a 52.5
a ≈ 0.27
S h =
( ) 0.27
h
298