Question

Finding the Domain and Range of a Graph.

Answer 1

The parenthesis versus bracket thing is very important when entering your answer.

Interval part:

Domain: (-5,5]

Range: (2,3]

Inequality part:

Domain:
`\-5<x\le 5\`

Range:
`\y`

Explanation:

For domain, you read the graph from left to right.

The domain is all the x's where the relation exists.

We see that the line starts at x=-5 and ends at x=5.

We are NOT going to include x=-5 because there is a hole; this means immediately after x=-5 does the line exist.

We are going to include x=5 because the whole is filled which means our relation exists for x=5.

So an interval notation the domain is (-5,5].

The parenthesis means not to include the endpoint where the bracket mean to include.

The range is the y values for where the relation exists so you look from bottom to top or down to up.

So we see the first y is at y=2 (again there doesn't exist a point at y=2 because of the hole so we are going to have a parenthesis here which means not to include).

Reading up from there we see the last y that is reached is y=3 and we do include that point because the hole is filled.

So the range in interval notation is (2,3].

Assume
`a` is a smaller value than
`b`.

Now if you have the variable u is in the interval
`(a,b)` then the inequality is
`a<u<b`.

If the interval was
`[a,b)` then it would be
`a \le u <b`

If the interval was
`[a,b]` then it would be
`a \le u le b`

If the interval was
`(a,b]` then it would be
`a<u \le b`

So if you haven't guessed it, if you see an equal part in your inequality than you will have a bracket for that number in the interval notation.

So let's look at our answers from above to find the inequality notation:

Domain: (-5,5]

Domain is the x's where the relation exists.

So this means we have
`\-5<x\le 5\`.

Range: (2,3]

Range is the y's where the relation exists:

So this means we have
`\2<y\le 3\`.