The domain of a function is the set of values that we are allowed to plug into our function.
The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in. They are the y values.
To represent the answer in interval notation, we should be aware of brackets.
( ) Open bracket
[ ] Close bracket
Interval Notation (-5, 3) [-5, 3] [-5, 3) |
Possible Values -4, -3, -2, -1, 0, 1, 2 -5, -4, -3, -2, -1, 0, 1, 2, 3 -5, -4, -3, -2, -1, 0, 1, 2 |
Find the domain and range range of each of the following functions. Express answers in interval notation.
Problem 1 :
Solution:
For what value of x the function is defined, first we have to check for what values of x the function is undefined.
For that, we have to equate the denominator to 0.
x + 2 = 0
x = -2
The domain is all real values except -2.
x ≠ -2
Domain:
(-∞, -2) ∪ (-2, ∞)
Range:
Problem 2 :
Solution:
For what value of x the function is defined, first we have to check for what values of x the function is undefined.
For that, we have to equate the denominator to 0.
x - 2 = 0
x = 2
The domain is all real values except 2.
x ≠ 2
Domain:
(-∞, 2) ∪ (2, ∞)
Range:
Problem 3 :
Solution:
For what value of x the function is defined, first we have to check for what values of x the function is undefined.
For that, we have to equate the denominator to 0.
x - 3 = 0
x = 3
The domain is all real values except 3.
x ≠ 3
Domain:
(-∞, 3) ∪ (3, ∞)
Range:
Problem 4 :
Solution:
For what value of x the function is defined, first we have to check for what values of x the function is undefined.
For that, we have to equate the denominator to 0.
x - 3 = 0
x = 3
The domain is all real values except 3.
x ≠ 3
Domain:
(-∞, 3) ∪ (3, ∞)
Range:
Problem 5 :
g(t) = |2x - 7| + 5
Solution:
g(t) = |2x - 7| + 5
Domain of g(t) is defined for all real values of x.
Domain:
(- ∞, ∞)
Range:
By analyzing the vertex of the absolute value function, we can figure out the range easily.
Vertex is at (7, 5). So, the range is [5, ∞)
Problem 6 :
h(t) = 6- |t - 1|
Solution:
h(t) = 6 - |t - 1|
h(t) = - |t - 1| + 6
The absolute value function opens down.
Domain of h(t) is defined for all real values of t.
Domain:
(- ∞, ∞)
Range:
h(t) = - |t - 1| + 6
Vertex is at (1, 6). So, the range is (-∞, 6].
Problem 7 :
Solution:
Domain:
The domain of function f defines by f(x) is the set of all real numbers.
Domain: (-∞, ∞)
Range:
The range of function is the set of all real numbers.
Range: (-∞, ∞)
Problem 6 :
Solution:
Domain:
Range:
[2, ∞)
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