Question

how do I find the domain of a graph, like what should I look for to find the two numbers for the domain, im confused

Answer 1

The domain is the set of allowed numbers as inputs

ie it's the set of x values that are allowed in the function

Answer 2

if there are any holes, jumps, gaps, or asymptotes, then you would exclude those x values from the domain because they aren't defined for that function

Answer 3

does that make sense?

Answer 4

so say the graph looked like this, im trying to understand what you just said, like I guess u meant, and sharp turns, or like drastic moves in the graph aren't allowed, so which part of this graph given would be considered the domain

Answer 5

sharp turns are allowed, just no holes, gaps, jumps or asymptotes

Answer 6

bc I don't see any jumps or gaps or anything in this graph so what the heck

Answer 7

the graph is defined for all x values between x = -4 (including -4) and x = 5 (excluding 5)

So the domain written as a compound inequality is: -4 <= x < 5

Answer 8

The domain of -4 <= x < 5 says to you that you can pick any number in that interval and plug it into f(x) to get some number out

try to plug in anything outside that interval and you wouldn't get a result because the function is undefined outside this interval

Answer 9

basically, the domain is just the collection of x values that work for the function

visually, the domain is the collection of x values that are part of the points that lie on the graph of f(x)

Answer 10

oh because that's where the graph ends, like that's the most any x-value can be on either side?

Answer 11

exactly, you can't go outside that interval...otherwise, what's the function output if you do?

Answer 12

since you can't answer that question with the graph, you must stay within the domain

Answer 13

is the domain all x valuea and the range is all y-values that you cant go beyond on either side?

Answer 14

yes the domain is the set of allowed x values

the range is the set of possible y values

Answer 15

domain: allowed inputs

range: possible outputs

Answer 16

so in this case, the range is 0 <= y <= 9 since the smallest y value possible is 0 and the largest possible is 9

Answer 17

okay that's more understandable!

Answer 18

glad it's all clicking now

Answer 19

and im re-doing quizzes to study for a big math test I have tomarrow so im trying to make sure I understand if anything, all of these concepts, and for this graph question, the same graph I attached, it asks me to find the zeros of (x,y) do u know how to do that also, like the steps you take to find that answer

Answer 20

the zeros or roots, are the points where the graph crosses the x axis

Answer 21

the graph crosses the x-axis only once and it looks like it's at the point (3,0)

So the x-intercept is (3,0) which means that the root is 3

So the only zero is 3

Answer 22

I prefer the term "root" over "zero" because a lot of people (including me sometimes) confuse the term with the actual number

Answer 23

okay that makes sense, is there a certain study habit you do that makes you understand math so much?

Answer 24

just practice practice practice

and try to translate everything into a language that you can understand

Answer 25

ex: I translated zero into root because I understand and work with that term easier

or another ex: domain is the collection of all allowed inputs or x values

Answer 26

yeah okay!i try to just dumb everything down and simplify it as much as I can so theres less I need to remember, im kind of naturally an idiot so it gets hard a lot. okay, next question, how do you find the maximum and minimum of a graph

Answer 27

you seem to be understanding this pretty well, so you're far from an idiot

Answer 28

minimum is the smallest y value

the minimum point is the point where the smallest y value occurs

Answer 29

the maximum is the largest y value

the maximum point is the point where the largest y value occurs

Answer 30

say we had this graph