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Absolute Value Function Worksheet - Page 2

Absolute Value Function Worksheet
  • Page 2
 11.  
Find the values of x, if |4x + 1| = 4 3.
a.
-1 12, 7 12
b.
1, -7
c.
1, 1 12
d.
1 12, -7 12


Solution:

|4x + 1| = 4 / 3

4x + 1 = 4 / 3 or 4x + 1 = -4 / 3
[The expression 4x + 1 is equal to -4 / 3 or 4 / 3.]

4x + 1 - 1 = 4 / 3 - 1 or 4x + 1 - 1 = -4 / 3 - 1
[Subtracting 1 from the two sides of the equation.]

4x = 1 / 3 or 4x = -7 / 3
[Simplify.]

x = 1 / 12 or x = -7 / 12
[Divide throughout by 4.]

The two solutions of the expression are 1 / 12 and -7 / 12.


Correct answer : (4)
 12.  
Find the values of x, if |4x - 16| - 19 = 12.
a.
47 4, 47 4
b.
47 4, -15 4
c.
47 4, 1 4
d.
-47 4, -15 4


Solution:

|4x - 16| - 19 = 12

|4x - 16| - 19 + 19 = 12 + 19
[Add 19 to both sides of the equation.]

|4x - 16| = 31
[Simplify.]

|4x - 16| = 31, 4x - 16 equals to 31 or - 31.

4x - 16 = 31 or 4x - 16 = - 31.

4x - 16 + 16 = 31 + 16 or 4x - 16 + 16 = - 31 + 16
[Add 16 to both sides of the equation.]

4x = 47 or 4x = -15
[Simplify.]

x = 47 / 4 or x = -15 / 4
[Divide throughout by 4.]

The equation has two solutions: 47 / 4 and -15 / 4.


Correct answer : (2)
 13.  
Find the values of x, if |11 - 6x| - 1 4 = 5.6.
a.
-0.86, 2.81
b.
0.86, 2.81
c.
0.86, -2.81
d.
-0.86, -2.81


Solution:

|11 - 6x| - 1 / 4 = 5.6

|11 - 6x| - 1 / 4 + 1 / 4 = 5.6 + 1 / 4
[Add 1 / 4 to both sides of the equation.]

|11 - 6x| = 5.6 + 0.25 = 5.85
[Simplify.]

|11 - 6x| = 5.85, 11 - 6x equals 5.85 or - 5.85.

11 - 6x = 5.85 or 11 - 6x = - 5.85

11 - 6x - 11 = 5.85 - 11 or 11 - 6x - 11 = - 5.85 - 11
[Subtracting 11 from the two sides of the equation.]

x = 0.86 or x = 2.81
[Simplify.]

The equation has two solutions: 0.86 and 2.81.


Correct answer : (2)
 14.  
Which of the following is an absolute value function?
a.
f(x) = |8x - 10|
b.
f(x) = 10x3 - 8x - 5
c.
f(x) = 10x - 5x+8
d.
f(x) = 10e8x+5


Solution:

f(x) = 10x3 - 8x - 5 is a cubic function.

f(x) = 10x - 5x+8 is a rational function.

f(x) = 10e8x+5 is an exponential function.

f(x) = |8x - 10| an absolute value function.


Correct answer : (1)
 15.  
0
a.
b = - 9 or b = - 14
b.
b = 4 or b = 9
c.
b = - 4 or b = - 14
d.
b = 4 or b = - 14


Solution:

|b + 5| = 9

b + 5 = 9 or b + 5 = - 9

b = 4 or b = - 14


Correct answer : (4)
 16.  
0
a.
a = 20
b.
a = 20 or a = - 30
c.
a = 105 or a = -151
d.
a = 29.2 or a = -19.2


Solution:

|5a + 25| - 2 = 123

|5a + 25| = 125
[Add 2 to both sides of the equation.]

5a + 25 = 125 or 5a + 25 = - 125
[Express as a disjunction.]

5a = 100 or 5a = - 150
[Subtracting 25 from the two sides of the equation.]

a = 20 or a = - 30
[Divide throughout by 5 .]


Correct answer : (2)
 17.  
0
a.
z = 65 or z = 6
b.
z = 33 5or z = - 6
c.
z = - 33 5 or z = - 44
d.
z = - 33 5 or z = 11


Solution:

|11 - 5z| = 44

11 - 5z = 44 or 11 - 5z = - 44

- 5z = 33 or - 5z = - 55
[Subtracting 11 from the two sides of the equation.]

z = - 33 / 5 or z = 11
[Divide throughout by 5.]


Correct answer : (4)
 18.  
Determine whether the statement is true or False: If y < 0, then |6 - y| = 6 + y
a.
True
b.
False


Solution:

let y = - a, where a is any positive real number.
[y < 0.]

|6 - (- a)| = 6 - a
[Replace y = - a in the given statement.]

|6 + a| = 6 - a

6 + a = 6 - a, which is always false because a > 0.
[|x| = x, if x is positive.]


Correct answer : (2)
 19.  
Determine whether the given statement is true or false: If x ≥ 0, then |x - 4| = 4 - x
a.
True
b.
False


Solution:

If x ≥ 0, then |x - 4| = 4 - x

Take one example x = 8, which is greater than zero.

|8 - 4| = 4 - 8

4 = - 4, which is not true.

Hence, the given statement is not true.


Correct answer : (2)
 20.  
Determine whether the given statement is True or false: If k ≤ 0, then |k - 3| = |3 - k|
a.
False
b.
True


Solution:

Since k ≤ 0, let k = - b, where ' b ' is any positive real number.

|- b - 3| = |3 - (- b)|
[Substitute the values.]

|- (b + 3)| = |3 + b|

|b + 3| = |b + 3|, which is true.
[|- k| = |k|.]

So, the given statement is true.


Correct answer : (2)

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