Domain Range Function Worksheet.docx
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Domain Range Function Worksheet Page 1 1. Find the domain of the function 16-x2−−−−−√4. a. [- 4, 0) b. (- 4, 4] c. [- 4, 4] d. [0, 4] e. [4, ∞] Solution: f(x) = 16-x24 [Original function.] Set 16 - x 2 greater than or equal to zero to make the expression under the fourth root, positive. 16 - x 2 ≥ 0, so x 2 - 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]. 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
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Transcript of Domain Range Function Worksheet.docx
Domain Range Function Worksheet Page 11.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].
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.
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, ).
4.Find the domain: f(x) = 2x+3|7x+6|a.(- 67, 0)
b.(- , 0) (0, )
c.(- 67, )
d.[- 67, 67]
e.(- , - 67) U (- 67, )
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, ).
5.Find the domain of the function f (x) = 8x2-3x2-10a.(- , 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, ).
6.Find the domain of the function f(x) = 7x-8a.[78, )
b.[- 87, )
c.[87, )
d.(87, ]
e.(87, )
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.]
x 8 / 7[Divide by 7 on both sides.]
So, the domain of the function is [8 / 7, ).
7.Find the domain of the function: y = 12-xa.[- , 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).
8.Find the domain: f (x) = (11x-2)54a.[112, )
b.[211, ]
c.(- , - 211)
d.[211, )
e.(211, )
Solution:f (x) = (11x-2)54[Original Function.]
Solve for x which makes the expression under the fourth root, positive.
11x - 2 0
x 2 / 11
The domain of the function is [2 / 11, ).
9.Find the domain of the function: f (x) = 9-4x3x-2a.(- 23, 94)
b.[23, 94)
c.(23, 94]
d.(23, 94)
e.[- 94, - 23]
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
x 9 / 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].
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, ).11.Find the domain of the function: f(x) = |x - 8|a.(- 8, 8)
b.all real numbers
c.(- , 8) (8, )
d.(- , - 8) (- 8, 8) (8, )
e.(- , - 8) (- 8, 8)
Solution:f(x) = |x - 8|[Original Function.]
f(x) is defined for all real values of x.[f(x) is an absolute value function.]
So, the domain of the function is the set of all real numbers.
12.Find the domain of the function: f(x) = - x6 + 1a.All real values of x except 1
b.All real values of x greater than 1
c.all real values of x less than 1
d.(- , - 1) (- 1, 1)
e.all real values of x
Solution:f(x) = - x6 + 1[Original Function.]
As there in no real number x such that f(x) is not defined.[f(x) is a polynomial function.]
So, the domain of the function is 'all real values of x'.
13.Find the domain of the function, f(x) = log2 (8 - x).a.all real values greater 8
b.[- 8, 8]
c.all real values less than 8
d.all real values except 8
e.all real values less than - 8
Solution:f(x) = log2 (8 - x)[Original function.]
f(x) is defined, if (8 - x) is positive.[Logarithmic function is defined only for positive real numbers.]
8 - x > 0
8 - x - 8 > 0 - 8[Subtract 8 from each side.]
- x > - 8
x < 8
So, the domain of the function is all real values less than 8.
14.Find the domain of the logarithmic function, f(x) = log2 (x + 11)2.a.All real numbers less than - 11
b.All real numbers less than 11
c.All real numbers except - 11
d.All real numbers
e.All real numbers greater than 11
Solution:f(x) = log2 (x + 11)2[Original logarithmic function.]
Logarithmic function is defined only for positive real numbers, so x + 11 0[(x + 11)2 0]
x - 11
So, the domain of the function is all real numbers except - 11.
15.Write the domain of the function in interval notation.f(x) = 5-xx+8a.(- , - 8) (- 8, 8)
b.[- 8, )
c.(- , 8) (8, )
d.[- 8, 8]
e.(- , - 8) (- 8, )
Solution:f(x) = 5-xx+8,[Original Function.]
The denominator of the rational expression cannot be zero but the numerator can be zero.
x + 8 0
x - 8
So, the domain of the function is all real numbers except - 8.
The domain can be written in interval notation as, (- , - 8) (- 8, ).
16.Find the domain of the function: f (x) = 9xx2-4x-12a.{x | x 6, x > - 2}
b.All x
c.{x | x < 6, x - 2}
d.{x | x 6, x - 2}
e.{x | x > 6}
Solution:f (x) = 9xx2-4x-12[Original Function.]
Set the expression in the denominator equal to zero to find the values of x that are to be excluded from the domain.
x2 - 4x - 12 = 0
(x - 6)(x + 2) = 0[Factor the quadratic equation.]
x - 6 = 0 or x + 2 = 0[Zero product property.]
x = 6 or x = - 2 [Solve for x.]
So, the domain is {x | x 6, x - 2}.
17.What is the range of the function shown in the graph?
a.(- , 5) (5, )
b.(- , 1) (1, )
c.(- , )
d.(- , - 2) (- 2, )
e.(- , - 1) (- 1, )
Solution:The y-coordinates of the points on the graph are all real numbers except 1.
So, the range of the function is (- , 1) (1, ).
18.Find the range of the function y = x + 2x.a.(- , - 3) (- 3, )
b.[- 3, 3]
c.(- , - 3] [3, )
d.(- , - 3) (- 3, 3) (3, )
e.(- , 3) (3, )
Solution:y = x + 2x[Original Function.]
Draw the graph of the function.
The y-coordinates of the points on the graph are either less than or equal to - 3 or greater than or equal to 3.
The range of the function in interval notation is (- , - 3] [3, ).
19.What is the range of the function shown in the graph?
a.(- , )
b.(- , 1] [1, )
c.(- , 1) (- 1, 1)
d.[2, )
e.[- , 2]
Solution:The y-coordinates of the points on the graph are all real numbers.
So, the range of the function is (- , ).
20.Find the range of the function f(x) = x+3.a.(- , - 3) (- 3, )
b.(0, )
c.(- , - 3]
d.(- , 0) (0, )
e.[0, )
Solution:f (x) = x+3[Original Function.]
The function f(x) is defined if x + 3 0, so x - 3
That is, the domain is the set of real numbers greater than or equal to - 3.
So, the range of the function is all real numbers greater than or equal to zero. That is [0, ).
Domain Range Function Worksheet Page 11.Find the domain of the function 16-x24.a.[- 4, 0)
b.(- 4, 4]
c.[- 4, 4]
d.[0, 4]
e.[4, ]
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
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, )
4.Find the domain: f(x) = 2x+3|7x+6|a.(- 67, 0)
b.(- , 0) (0, )
c.(- 67, )
d.[- 67, 67]
e.(- , - 67) U (- 67, )
5.Find the domain of the function f (x) = 8x2-3x2-10a.(- , 10) (10, )
b.(- , )
c.(- , 0) (0, )
d.[- 10, 10]
e.(- , - 10) (10, )
6.Find the domain of the function f(x) = 7x-8a.[78, )
b.[- 87, )
c.[87, )
d.(87, ]
e.(87, )
7.Find the domain of the function: y = 12-xa.[- , 2]
b.(2, )
c.[- , 2)
d.(- , - 2) (- 2, )
e.(- , 2)
8.Find the domain: f (x) = (11x-2)54a.[112, )
b.[211, ]
c.(- , - 211)
d.[211, )
e.(211, )
9.Find the domain of the function: f (x) = 9-4x3x-2a.(- 23, 94)
b.[23, 94)
c.(23, 94]
d.(23, 94)
e.[- 94, - 23]
10.What is the range of the function shown in the graph?
a.[0, )
b.(- , 4) (4, )
c.(0, )
d.(- , 0) (0, )
e.[4, ]
11.Find the domain of the function: f(x) = |x - 8|a.(- 8, 8)
b.all real numbers
c.(- , 8) (8, )
d.(- , - 8) (- 8, 8) (8, )
e.(- , - 8) (- 8, 8)
12.Find the domain of the function: f(x) = - x6 + 1a.All real values of x except 1
b.All real values of x greater than 1
c.all real values of x less than 1
d.(- , - 1) (- 1, 1)
e.all real values of x
13.Find the domain of the function, f(x) = log2 (8 - x).a.all real values greater 8
b.[- 8, 8]
c.all real values less than 8
d.all real values except 8
e.all real values less than - 8
14.Find the domain of the logarithmic function, f(x) = log2 (x + 11)2.a.All real numbers less than - 11
b.All real numbers less than 11
c.All real numbers except - 11
d.All real numbers
e.All real numbers greater than 11
15.Write the domain of the function in interval notation.f(x) = 5-xx+8a.(- , - 8) (- 8, 8)
b.[- 8, )
c.(- , 8) (8, )
d.[- 8, 8]
e.(- , - 8) (- 8, )
16.Find the domain of the function: f (x) = 9xx2-4x-12a.{x | x 6, x > - 2}
b.All x
c.{x | x < 6, x - 2}
d.{x | x 6, x - 2}
e.{x | x > 6}
17.What is the range of the function shown in the graph?
a.(- , 5) (5, )
b.(- , 1) (1, )
c.(- , )
d.(- , - 2) (- 2, )
e.(- , - 1) (- 1, )
18.Find the range of the function y = x + 2x.a.(- , - 3) (- 3, )
b.[- 3, 3]
c.(- , - 3] [3, )
d.(- , - 3) (- 3, 3) (3, )
e.(- , 3) (3, )
19.What is the range of the function shown in the graph?
a.(- , )
b.(- , 1] [1, )
c.(- , 1) (- 1, 1)
d.[2, )
e.[- , 2]
20.Find the range of the function f(x) = x+3.a.(- , - 3) (- 3, )
b.(0, )
c.(- , - 3]
d.(- , 0) (0, )
e.[0, )
