Question

I need help in Precalculus on finding the domain and range given a graph. Could anyone please help me?

Answer 1

Go ahead and post the full question please.

Answer 2

thanks

Answer 3

let's focus on the first piece (the straight line)

Answer 4

any ideas what the domain would be here?

Answer 5

if you aren't sure, draw vertical lines that go from the orange graph until you reach the x axis

like you see in the attached image

Answer 6

the places where those blue lines touch the x axis will determine the domain

Answer 7

well part of the domain anyway

Answer 8

So -3?

Answer 9

What is the smallest x value in that region?

Answer 10

Do the blue lines make sense? The idea is to shade the x axis that corresponds to the graph.

Answer 11

The smallest point is the (-6,-3)

Answer 12

Which is not included in the function.. right?

Answer 13

(-6,-3) has an x coordinate of -6

so -6 is the smallest value in the domain

however, the open circle means we do NOT include x = -6 as part of the domain

ie x > -6

Answer 14

`Which is not included in the function.. right?`
that is correct
x = -6 is not part of the domain

Answer 15

Hopefully you're able to see how I shaded the x axis in that way?

Answer 16

Yes

Answer 17

ok great. Are you able to determine the domain from the shaded graph on the number line like that?

Answer 18

Look at the blue shaded region on the x axis. Where is the open circle? At what x value?

http://assets.openstudy.com/updates/attachments/57bf66d6e4b0ff8c9301b78f-jim_thompson5910-1472162402643-screenshot_10.png

Answer 19

(5,3)?

Answer 20

If you started at x = 0, which is where the y axis is at, then move 6 units to the left, you would get to the open circle

agreed?

Answer 21

Ohhh, yes. Agreed.

Answer 22

So the open circle is on the x axis at x = -6

Answer 23

where is the closed circle at? The closed circle for the first left blue segment on the x axis

Answer 24

3

Answer 25

not sure how you got 3

Answer 26

see attached

Answer 27

I was looking at the point on the other side, this is (-1,2)

Answer 28

(-1,0) actually

Answer 29

oh you're looking at the orange point

Answer 30

well the x coordinate is x = -1

Answer 31

so hopefully you see how that first blue segment starts at x = -6 and goes to x = -1 ?

Answer 32

Yup

Answer 33

so the domain for that piece is \(\Large -6 < x \le -1\)

In interval notation, we would say the domain for that piece is \(\Large (-6, -1]\)

The parenthesis says "exclude this endpoint"
The square bracket says "include this endpoint"

Answer 34

make sense?

Answer 35

Yeah, so the next one is 1 to 5

Answer 36

how would we write this in interval notation?

Answer 37

(1,5]

Answer 38

good

Answer 39

so "glue" those two pieces together to get this full domain \(\Large (-6, -1] \cup (1,5]\)

Answer 40

the U means "union" which is like saying "this interval or this interval"

Answer 41

So it has to be answer choice 'b'. Thank you so much for explaining it to me (even though it took a little while) it actually makes sense now!

Answer 42

You're welcome. Hopefully you see how the range is the same idea, but now on the y axis this time?

Answer 43

Yes :) thank you

Answer 44

ok great, glad to be of help