Solving Square Root Functions Worksheet

Solving Square Root Functions Worksheet
  • Page 1
 1.  
Simplify:
192

a.
53
b.
25
c.
37
d.
83


Solution:

192
[ Original expression.]

= (64×3)
[Factor 192 as 64 × 3.]

= (3×(82))

= 83


Correct answer : (4)
 2.  
Simplify:
162

a.
32
b.
56
c.
92
d.
23


Solution:

162
[ Original expression.]

= (81×2)
[Factor 162 as 81 × 2.]

= (2×(92))

92


Correct answer : (3)
 3.  
Simplify:
48

a.
43
b.
32
c.
23
d.
34


Solution:

48
[ Original expression.]

= (16×3)
[Factor 48 as 16 × 3.]

= (3×(42))

= 43


Correct answer : (1)
 4.  
Simplify:
72

a.
36
b.
53
c.
26
d.
62


Solution:

72
[Original expression.]

= (36×2)
[Factor 72 as 36 × 2.]

= (2×(62))

= 62


Correct answer : (4)
 5.  
Simplify:
28
a.
27
b.
37
c.
73
d.
32


Solution:

28
[Original expression.]

=7 × 4
[Factor 28 as 7 × 4.]

=7×(22)

=27


Correct answer : (1)
 6.  
Find the domain and the range of y = x8x.
a.
Both domain and range are all negative real numbers.
b.
Both domain and range are all non-negative real numbers.
c.
Domain: all real numbers greater than or equal to 8; range: all non-negative real numbers.
d.
Domain: all non-negative real numbers; range: all real numbers greater than or equal to 8.


Solution:

Find the values of x for which the function is defined.

The function x8x exists only for 8x ≥ 0 x ≥ 0.

The domain is the set of all non-negative real numbers.

The range of the function is the set of all non-negative real numbers.


Correct answer : (2)
 7.  
Which of the following functions best represents the graph?

a.
y = x + 7
b.
y = 2x + 5
c.
y = 2x + 1
d.
y = x + 7


Solution:

On the graph, (2, 3) and (- 3, 2) points are marked. So, the function representing the graph should satisfy these two points.

Consider the function y = x + 7, if x = 2 then y = 8.414. So, this is not the required function.

Consider the function y = 2x + 5, if x = 2, then y = 3 and when x = - 3, then y is undefined. So, this is not the required function.

Consider the function y = 2x + 1, if x = 2, then y = 3 and when x = - 3, then y is undefined. So, this is not the required function.

Consider the function y = x + 7, if x = 2, then y = 3 and when x = - 3, then y = 2. So, this is the required function.


Correct answer : (4)
 8.  
Which of the following functions best represents the graph?

a.
x - 2x
b.
x - 4
c.
x - 4x
d.
4x - 1


Solution:

The two points on the graph (1, - 1) and (4, 0) satisfy the funciton x - 2x.


Correct answer : (1)
 9.  
The period T in seconds and the length L in inches of the pendulum are related as T = 2πL384. Find the length of the pendulum in inches with period of 6 seconds.
a.
350.17
b.
102.76
c.
580.64
d.
298.32


Solution:

T = 2πL384

T2 = (2π)2L384
[Square on both sides.]

384 · T2 = (2π)2L
[Multiply both sides with 384.]

L = T2384(2π)2
[Divide both sides by (2π )2.]

L = (6)2384(2π)2
[Substitute 6 for T.]

L = 350.17 inches.

The length of the pendulum = 350.17 inches.


Correct answer : (1)
 10.  
Find the lateral surface area s of a cone whose base radius r is 3 cm and height h is 4 cm.
Use the formula s = π r r2 +h2.
a.
5π sq.cm.
b.
15π sq.cm.
c.
8π sq.cm.
d.
24π sq.cm.


Solution:

s = π r r2 +h2

= 3π 9 + 16
[Replace r with 3 and h with 4.]

= 15π sq.cm.


Correct answer : (2)

*AP and SAT are registered trademarks of the College Board.