Finding the Domain and Range of a Graph.

Accepted Solution

Answer:The parenthesis versus bracket thing is very important when entering your answer.Interval part:Domain: (-5,5]Range: (2,3]Inequality part: Domain: [tex]\{x|-5<x\le 5\}[/tex]Range: [tex]\{y|2<y\le 3\}[/tex]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 [tex]a[/tex] is a smaller value than [tex]b[/tex].Now if you have the variable u is in the  interval [tex](a,b)[/tex] then the inequality is [tex]a<u<b[/tex]. If the interval was [tex][a,b)[/tex] then it would be [tex]a \le u <b[/tex]If the interval was [tex][a,b][/tex] then it would be [tex]a \le u le b[/tex]If the interval was [tex](a,b][/tex] then it would be [tex]a<u \le b[/tex]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 [tex]\{x|-5<x\le 5\}[/tex].Range: (2,3]Range is the y's where the relation exists:So this means we have [tex]\{y|2<y\le 3\}[/tex].