Math graphing help. Medals.

- theopenstudyowl

Math graphing help. Medals.

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- theopenstudyowl

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##### 2 Attachments

- theopenstudyowl

Its #4 only

- theopenstudyowl

Anything?

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## More answers

- jim_thompson5910

For #4, draw a vertical line through -4 on the x axis
where does this vertical line cross the red f(x) curve?

- theopenstudyowl

@ (-2,1) and (2,2)

- theopenstudyowl

oh wait, sorry those are the points of intersection of the two functions, one sec.

- theopenstudyowl

at x=3

- jim_thompson5910

see attached

##### 1 Attachment

- theopenstudyowl

does this have to do with the vertical line test?

- jim_thompson5910

no, I'm simply asking for the value of f(-4)

- theopenstudyowl

oh

- theopenstudyowl

Ok, could you help me with the domain and range part of the problem please.?

- jim_thompson5910

so you figured out that part already? the f(-4) part?

- theopenstudyowl

that wasnt the part I needed help with.. just included it because the graph is required in order to understand the rest of the problem..

- jim_thompson5910

I see

- jim_thompson5910

the domain is the set of allowed inputs, in other words, the set of allowed x values

- theopenstudyowl

ok...

- jim_thompson5910

the red f(x) function stretches from x = -4 to x = 4
the function is not defined for other x values (like x = 10)

- jim_thompson5910

so that's why the domain is \[\Large -4 \le x \le 4\]
in interval notation, the domain is written as `[-4, 4]` Notice the use of square brackets to mean include the endpoints

- jim_thompson5910

what would be the domain of g(x) ?

- theopenstudyowl

ok, I'll solve that now, could you explain to me when I include brackets and parenthesis when writing these things..?

- theopenstudyowl

The domain of g(x) is [-4,3]

- jim_thompson5910

the parenthesis are used to exclude the endpoint
that's when you come across an endpoint with an open circle like so
|dw:1440727842554:dw|

- jim_thompson5910

|dw:1440727856238:dw|

- jim_thompson5910

think of it as like a road that isn't finished. There is a pot hole at the open circle. It is NOT included in part of the road because you can't drive on it

- theopenstudyowl

So when there is a circle, I use brackets?

- theopenstudyowl

oh wait parenthesis nvm

- jim_thompson5910

|dw:1440728130377:dw|

- theopenstudyowl

ok thanks, could you help me with the range too plz?

- jim_thompson5910

the range is the set of possible outputs of a function
put another way, the range is the set of possible y values that could come out

- jim_thompson5910

look at the red curve f(x)
the lowest it goes is to y = -2
the highest it goes is to y = 3
the range of f(x) is \[\Large -2 \le y \le 3\]
in interval notation the range of f(x) is `[-2,3]`
I'll let you do g(x)

- theopenstudyowl

ok, is my domain for g(x) correct?

- jim_thompson5910

what did you say for the domain of g(x)?

- jim_thompson5910

oh nvm, you wrote `The domain of g(x) is [-4,3]`

- jim_thompson5910

yeah that is correct

- theopenstudyowl

yah!

- theopenstudyowl

ok, give me a sec for the other one...

- theopenstudyowl

1/2 is less than or equal to y is less than or equal to 4

- jim_thompson5910

I don't agree with the 1/2 part

- jim_thompson5910

oh wait, nvm

- jim_thompson5910

each tick is 1

- theopenstudyowl

its hard to tell

- jim_thompson5910

1/2 is a good estimate

- jim_thompson5910

what would the range be in interval notation?

- theopenstudyowl

[1/2,4]

- theopenstudyowl

?

- jim_thompson5910

correct

- theopenstudyowl

ok, cool, Could you explain to me when I use less than and less than or equal to, is there a clear way of knowing?

- jim_thompson5910

it depends on if you have open or closed circles
|dw:1440728925694:dw|

- jim_thompson5910

when you include a point, you say "or equal to"
eg: \[\Large x \le 5\] we're including 5

- jim_thompson5910

saying `x > 5` we mean everything larger than 5 and we exclude 5 from the set

- theopenstudyowl

ok cool, thanks!

- jim_thompson5910

sure thing

- theopenstudyowl

http://assets.openstudy.com/updates/attachments/55dfbcb4e4b0819646d75855-theopenstudyowl-1440726228078-unnamed.jpg
http://assets.openstudy.com/updates/attachments/55dfbcb4e4b0819646d75855-theopenstudyowl-1440726228718-unnamed1.jpg

- theopenstudyowl

a) f(-4)=-2, g(3)=4.
b) The values of x where f(x)=g(x) are x=-2 and x=2.
c) An estimation of the solution of the equation f(x)=-1, is x=3.
d) The interval on what f is decreasing is [0,4].
e) The domain of f(x) is [-4,4], the range of f(x) is [-2,3].
f) The domain of g(x) is [-4,3], the range of g(x) is [1/2,4].

- theopenstudyowl

@jim_thompson5910 does anything look incorrect?

- jim_thompson5910

`c) An estimation of the solution of the equation f(x)=-1, is x=3.`
there's one other solution

- theopenstudyowl

ok

- jim_thompson5910

`d) The interval on what f is decreasing is [0,4].`
f is not decreasing when x = 0 or at the endpoint x = 4
so you'll need to exclude the endpoints and say \(\Large (0,4)\)

- theopenstudyowl

ok cool, does everything else look ok?

- jim_thompson5910

everything else is perfect

- theopenstudyowl

ok, and for c, how would I find that other point?

- jim_thompson5910

draw a horizontal line through y = -1 and see where it crosses the red f(x) function

- jim_thompson5910

you already found (3,-1)

- jim_thompson5910

actually I think you meant to say (-3,-1)

- jim_thompson5910

if f(x) = -1, then x = -3 or x = ???

- theopenstudyowl

one sec

- theopenstudyowl

and 4?

- jim_thompson5910

yep

- theopenstudyowl

so its x=-3 and 4?

- jim_thompson5910

yes if f(x) = -1, then x = -3 or x = 4

- theopenstudyowl

ok great, well thanks again for your wonderful help. Saved me alot of time, hope you have an awesome rest of your day!

- jim_thompson5910

glad to be of help

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