Question

Finding the Domain and Range of a Graph.

Answer 1

Answer:

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

Interval part:

Domain: (-5,5]

Range: (2,3]

Inequality part:

Domain: $\{x|-5<x\le 5\}$

Range: $\{y|2<y\le 3\}$

Step-by-step 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 $\{x|-5<x\le 5\}$.

Range: (2,3]

Range is the y's where the relation exists:

So this means we have $\{y|2<y\le 3\}$.