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Domain Range Function Worksheet

Domain Range Function Worksheet
  • Page 1
 1.  
Find the domain of the function 16-x24.
a.
[- 4, 0)
b.
(- 4, 4]
c.
[- 4, 4]
d.
[0, 4]
e.
[4, ∞]


Solution:

f(x) = 16-x24
[Original function.]

Set 16 - x2 greater than or equal to zero to make the expression under the fourth root, positive.

16 - x2 ≥ 0, so x2 - 16 ≤ 0

(x - 4)(x + 4) ≤ 0
[Factor the left side of the inequality.]

x ≥ - 4 and x ≤ 4

So, the domain of the function is [- 4, 4].


Correct answer : (3)
 2.  
Find the domain of the function, f(x) = - -4x+5.
a.
All real values of x
b.
All real values of x ≤ - 1.25
c.
All real values of x ≥ 1.25
d.
All real values of x except 1.25
e.
All real values of x ≤ 1.25


Solution:

f(x) = - -4x+5
[Original function.]

f(x) is defined if - 4x + 5 ≥ 0

- 4x ≥ - 5
[Subtract 5 from both sides.]

4x ≤ 5
[Divide by - 1.]

x ≤ 1.25
[Divide by 4 on both sides.]

So, the domain is all real values of x less than or equal to 1.25.


Correct answer : (5)
 3.  
Find the domain of the function, f(x) = x+6x2+10x+9.
a.
(- ∞, - 9) (- 1, ∞)
b.
[- 9, - 1]
c.
(- 9, - 1) (- 1, ∞)
d.
(- ∞, - 9) (- 9, - 1)
e.
(- ∞, - 9) (- 9, - 1) (- 1, ∞)


Solution:

f(x) = x+6x2+10x+9
[Original function.]

f (x) = x+6(x+9)(x+1)
[Factor the denominator.]

Set the denominator equal to zero to solve for x.

(x + 9) (x + 1) = 0

x = - 9, x = - 1

That is f(x) is not defined at x = - 9 and at x = - 1

So, the domain of the function is (- ∞, - 9) (- 9, - 1) (- 1, ∞).


Correct answer : (5)
 4.  
Find the domain: f(x) = 2x+3|7x+6|
a.
(- 6 7, 0)
b.
(- ∞, 0) (0, ∞)
c.
(- 6 7, ∞)
d.
[- 6 7, 6 7]
e.
(- ∞, - 6 7) U (- 6 7, ∞)


Solution:

f(x) = 2x+3|7x+6|
[Original function.]

Set the denominator equal to zero to solve for x.

7x + 6 = 0

x = - 6 / 7

That is f(x) is not defined at x = - 6 / 7.

So, the domain of the function f is (- ∞, - 6 / 7) (- 6 / 7, ∞).


Correct answer : (5)
 5.  
Find the domain of the function f (x) = 8x2-3x2-10
a.
(- ∞, 10) (10, ∞)
b.
(- ∞, ∞)
c.
(- ∞, 0) (0, ∞)
d.
[- 10, 10]
e.
(- ∞, - 10) (10, ∞)


Solution:

f (x) = 8x2-3x2-10
[Original Function.]

Solve for x which makes the expression under the square root, positive.

x2 - 10 > 0

(x - 10)(x + 10) > 0
[Factor the left side of the inequality.]

x < - 10 or x > 10

So, the domain of the function is (- ∞, - 10) (10, ∞).


Correct answer : (5)
 6.  
Find the domain of the function f(x) = 7x-8
a.
[7 8, ∞)
b.
[- 8 7, ∞)
c.
[8 7, ∞)
d.
(8 7, ∞]
e.
(8 7, ∞)


Solution:

f(x) = 7x-8
[Original Function.]

Solve for x which makes the expression under the square root, positive.

7x - 8 ≥ 0

7x ≥ 8
[Add 8 on both sides.]

x8 / 7
[Divide by 7 on both sides.]

So, the domain of the function is [8 / 7, ∞).


Correct answer : (3)
 7.  
Find the domain of the function: y = 12-x
a.
[- ∞, 2]
b.
(2, ∞)
c.
[- ∞, 2)
d.
(- ∞, - 2) (- 2, ∞)
e.
(- ∞, 2)


Solution:

y = 12-x
[Original Function.]

Solve for x which makes the expression under the square root, positive.

2 - x > 0

2 > x
[Add x on both sides.]

So, the domain of the function is (- ∞, 2).


Correct answer : (5)
 8.  
Find the domain: f (x) = (11x-2)54
a.
[11 2, ∞)
b.
[2 11, ∞]
c.
(- ∞, - 2 11)
d.
[2 11, ∞)
e.
(2 11, ∞)


Solution:

f (x) = (11x-2)54
[Original Function.]

Solve for x which makes the expression under the fourth root, positive.

11x - 2 ≥ 0

x2 / 11

The domain of the function is [2 / 11, ∞).


Correct answer : (4)
 9.  
Find the domain of the function: f (x) = 9-4x3x-2
a.
(- 2 3, 9 4)
b.
[2 3, 9 4)
c.
(2 3, 9 4]
d.
(2 3, 9 4)
e.
[- 9 4, - 2 3]


Solution:

f (x) = 9-4x3x-2
[Original Function.]

Solve for x which makes the expression under the square root in the numerator, positive.

9 - 4x ≥ 0

x9 / 4

Solve for x which makes the expression under the square root in the denominator, positive.

3x - 2 > 0

x > 2 / 3

So, the domain of the function is (2 / 3, 9 / 4].


Correct answer : (3)
 10.  
What is the range of the function shown in the graph?


a.
[0, ∞)
b.
(- ∞, 4) (4, ∞)
c.
(0, ∞)
d.
(- ∞, 0) (0, ∞)
e.
[4, ∞]


Solution:

The y-coordinates of the points on the graph are all real numbers greater than or equal to zero.

So, the range of the function is [0, ∞).


Correct answer : (1)

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