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Function Worksheets - Page 4

Function Worksheets
  • Page 4
 31.  
Find the domain of the function f(x) = 7 - x.
a.
(- ∞, 7]
b.
(- ∞, 7)
c.
(- ∞, ∞)
d.
[7, ∞)


Solution:

f(x) = 7 - x

In order to have f(x) = 7 - x as a real number, we must have 7 - x ≥ 0 or x ≤ 7. Thus the domain of f(x) is [7, ∞)


Correct answer : (4)
 32.  
Find the domain of the function f(x) = 12 - x.
a.
(- ∞, 2)
b.
(- ∞, ∞)
c.
(2, ∞)
d.
(- ∞, 2]


Solution:

f(x) = 12 - x

In order to have f(x) = 12 - x as a real number we must have 2 - x > 0 or x < 2

So, the domain of f( x) is D = (- ∞, 2)


Correct answer : (1)
 33.  
Find the domain of the function f(x) = x2 - 12x + 32.
a.
(- ∞, ∞)
b.
(4, 8)
c.
(- ∞, 8) (8, ∞)
d.
(- ∞, 4] [8, ∞)


Solution:

f(x) = x2 - 12x + 32 = (x - 4 )(x - 8)

In order to have f(x) = x2 - 12x + 32 = (x - 4)(x - 8) as a real number we must have (x - 4) (x - 8) ≥ 0

x (- ∞, 4] [8, ∞)
[Solve the inequality.]

So, the domain of f(x) = D = (- ∞, 4] [8, ∞)


Correct answer : (4)
 34.  
Find the domain of the function f(x) = 1x2 - 11x + 24.
a.
(- ∞, 3) (8, ∞)
b.
(- ∞, 8)
c.
(- ∞, 3]
d.
[8, ∞)


Solution:

f(x) = 1x2 - 11x + 24 = 1(x - 8)(x - 3)

In order to have f(x) = 1(x - 8)(x - 3) as a real number, we must have (x - 8)(x - 3) > 0

x (- ∞, 3) (8, ∞)
[Solve the inequality.]

So, the domain of f(x) = (- ∞, 3) (8, ∞)


Correct answer : (1)
 35.  
Find the domain of the function f(x) =6 - xx - 7.
a.
[6, 7)
b.
(6, 7]
c.
(- ∞, ∞)
d.
[6, 7]


Solution:

f(x) = 6 - xx - 7

In order to have f(x) = 6 - xx - 7 as a real number we must have 6 - xx - 7 ≥ 0 or (6 - x) (x - 7) ≥ 0 and x ≠ 7

(x - 6) (x - 7) ≤ 0 and x ≠ 7

x [6, 7)
[Solve the inequality.]


Correct answer : (1)
 36.  
Which of the following is the largest domain of the function f(x) = x2 + 2?
a.
(- ∞, ∞)
b.
(- 2, 2)
c.
(2, ∞)
d.
(- ∞, 2)


Solution:

f(x) = x2 + 2

= |x| + 2
[Use x2 = |x|.]

Since |x| + 2 is a real number for every real x, the domain of f(x) = D = (- ∞, ∞)


Correct answer : (1)
 37.  
Find the domain of the function f(x) = x2 - 9x - 3.
a.
(- ∞, 3]
b.
(- ∞, ∞)
c.
(- ∞, 3) (3, ∞)
d.
[3, ∞)


Solution:

f(x) = x2 - 9x - 3

The function f(x) is not defined at x = 3.

So, the domain of f(x) is all real numbers except 3

That is the domain of the function f(x) in the intervel notation is (- ∞, 3) (3, ∞)


Correct answer : (3)
 38.  
The graph of the function rule intersect the y-axis at (0, 13). Which of the following is true about the coordinates of the point?
a.
Input = 13, Output = 13
b.
Input = 0, Output = 13
c.
Input = 13, Output = 0
d.
Input = 0, Output = 0


Solution:

The graph of the function rule intersect the y-axis at (0, 13) means the function output is 13 for an input of 0.


Correct answer : (2)
 39.  
Objective : Represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities including representations involving computer algebra systems, spreadsheets, and graphing calculators.
Which table describe the function f(x) = - 2x + 1, if x = 0, 1, 2, 3?

a.
Table - 1
b.
Table - 2
c.
Table - 4
d.
Table - 3


Answer: (a)


Correct answer : (1)
 40.  
Identify the equation that represents the table.
x0248
y2346
a.
y = 2x - 1
b.
y = x + 2
c.
y = 1 2x + 2
d.
y = 2(x - 1)


Answer: (c)


Correct answer : (3)

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