How To Find Out Who Reported You On Domain_6

Find the domain of a graph of a part; examples with solutions are presented. First the graphical significant of the concept of the domain of a part is explained.

Domain of a Graph of a Function

The implied domain of a role f is the gear up of all values of x for which f(x) is defined and real. The graph of a part f is the set of all points (x , f(x)). Hence, For a office f defined by its graph, the implied domain of f is the set of all the real values 10 along the ten-axis for which there is a point on the given graph.
Every bit an example there are points on the graph below at x = - 3, - 2.5, -2, -0.5 , 2,five, three, iii.2, 4. These values and more than other values of 10 are included in the domain of f.
There are no points on the graph at x = - one (open circle on the graph) , 0.5 , 1, ane.5 , two (open circle). These values and more other values of x are not included in the domain. graph of functions domain explanations

With these ideas and definition, we will now solve examples where the whole domain of a given graph is found.

Domain of a Graph; Examples with Detailed Solutions

Example ane

Find the domain of the graph of the function shown below and write it in both interval and inequality notations.

find domain of graph of function for example 1

Solution to Example 1

The graph starts at x = - 4 and ends x = half dozen. For all x betwixt -4 and 6, there points on the graph. Hence the domain, in interval note, is written equally
[-4 , 6]
In inequality notation, the domain is written equally
- four ≤ x ≤ half-dozen
Note that we close the brackets of the interval because -4 and half dozen are included in the domain which is indicated by the closed circles at 10 = - 4 and 10 = 6.

Example ii

What is the domain, in interval annotation, of the graph of the function shown below?

find domain of graph of function for example 2

Solution to Example ii

The graph starts at x = - four and ends x = 4. In that location are points on the graph for all values of ten between - iv and four including at - iv and four. Hence the domain, in interval note, is written every bit
[ - 4 , 4]

Example three

What is the domain of the graph of the function?

find domain of graph of function for example 3

Solution to Instance 3

The graph starts at x = - 8 and ends ten = 8. The graph is defined for all x between - 8 and viii. We include - 8 and eight because of the airtight circles at x = - 8 and x = 8. Hence the domain, in interval notation, is written as
[ - 8 , 8]

Example 4

Find the domain of the graph of the function shown beneath.

find domain of graph of function for example 4

Solution to Case iv

The graph starts at x = - 4 and ends x = 6. The graph is defined for all ten between - 4 and 6. The interval is closed at - iv and half dozen because of the closed circles at x = - four and ten = 6. Hence the domain, in interval notation is written every bit
[- 4 , six]

Example 5

Write the domain of the graph of the function shown below in interval and inequality notations.

find domain of graph of function for example 5

Solution to Example 5

The graph starts at values of x > - 4 and ends at values of ten < 4. x = - iv and x = 4 are not included in the domain because of the open circles at these values. Hence the domain, in interval notation, is written every bit
( - 4 , 6 )
Notation that the interval is open to indicate that - iv and 4 are non included in the domain of the graph.
In inequality note, the aforementioned domain is given by
- 4 < ten < six
Note that the strict inequality sign (without equal) is used in the inequality notation of the domain considering ten = - four and x = 6 are not included in the domain.

Instance 6

Write the domain of the graph of the function shown below in interval notation.

find domain of graph of function for example 6

Solution to Example 6

The graph starts at values of x = - 8 and ends at values of x < 2. The open circles at 10 = - 4, x = -2 and ten = 2 indicates that these values are not included in the domain. Hence the domain, in interval notation, is written as
[ - 8 , - 4 ) ∪ (- 4 , -2) ∪ (-ii , 2)
Note the interval is open at x = - 4, x = -2 and ten = ii to indicate that these values are non included in the domain of the graph.

Example seven

Write the domain of the graph of the function shown below in inequality notation.

find domain of graph of function for example 7

Solution to Example 7
The graph starts at ten = - 4 and ends x < 2. The domain does not include x = two because of the open circle at x = 2. Hence the domain, in inequality note, is written equally
- 4 ≤ 10 < 2

Case eight

Write the domain of the graph of the part shown below using interval notation

find domain of graph of function for example 8

Solution to Example 8

The graph is made up of three parts. The left part is defined for all values of ten between - iv and - 2. The part in the centre is defined on the interval x > 0 and x ≤ 4. The office on the right is defined for x > half-dozen and x ≤ vi. The domain is written equally a union of iii intervals every bit follows
[ - 4 , -2 ] ∪ (0 , iv] ∪ (6 , 8]