Question

calculus 1 ! limits, graph with continuous intervals! someone help me !

Answer 1

What do you need help with?

Answer 2

i need indicate where f(x) is continuous.

Answer 3

What is f(x)

Answer 4

this is the graph!

Answer 5

Do you know the three rules to check for continuity?

Answer 6

uhm yeah but im not sure to understand them

Answer 7

Basically what you need to do is look at any point on the graph, check on either side of that point, if the y-values on either side are the same then check to see if the y-value of the point is the same as the ones one either side. Going from left to right on the graph, we can see potential discontinuities at -1, 0, 1, and 3 so just check these points Which ones are discontinuous?

Answer 8

-1 and 0

Answer 9

idk haha

Answer 10

Alright, lets take it one by one. Discontinuities happen in three ways, either a hole in the graph, a break where the graph "jumps" or if the graph goes off to infinity. The first place we see this on the graph is -1. With me so far?

Answer 11

ok yeah so we dont care abu the hole at -2

Answer 12

The hole at negative 2 is just the start of the function so we an ignore it for now. At -1, though, we have to do our tests. 1st test is f(c) defined? (c=-1 in this case)

Answer 13

ok , uhm i think it is

Answer 14

You're right cuz at -1 the y-value is 4, if there were no y-value or the y-value was infinity then the point would fail at this part of the test. Got it?

Answer 15

oh ok yeah !

Answer 16

i understand a little bit more thanks

Answer 17

Test 2, does the limit exist here? so basically see if the stuff to the left and right of this point meet up

Answer 18

i dont think so

Answer 19

hmmm. let me try explaining he whole thing a different way cuz I don't think I'm explaining it well this way.

Answer 20

haha im dumb dont worry , it<s not u lol

Answer 21

Discontinuities show up in three different ways, they either are holes in the graph, like at -1, they are jumps in the graph like at 1, or the graph goes to infinity like at 0, see each of those examples?

Answer 22

yes i see

Answer 23

Okay so these are the discontinuities of the graph, you don't have to really bother with the tests if you know these three ways that discontinuities show up. Basically the function is continuous between its endpoints except for at -1, 0, and 1 because it is discontinuous here so find the endpoints

Answer 24

ok i let me think 2 sec

Answer 25

so they intervals of continuity will be

Answer 26

between each of the discontinuities

Answer 27

the first interval is from -2 to -1 or [-2,-1) because the function starts at -2 and the first discontinuity is at -1, then next one will be (-1,0) because the first discontinuity is -1 and the next one is 0 etc.

Answer 28

and the third one from (1,4]?

Answer 29

Exactly but you skipped the one between 0 and 1 but I think you understand it now!

Answer 30

yeah so from (0,1)?!

Answer 31

There you go

Answer 32

omg thanks wait ill see if that works in webwork (my math hw)!

Answer 33

HALLELLUYA thank u so much ssullivan !!

Answer 34

No problem

Answer 35

if i need your help in the future are u going on this site often?