theopenstudyowl
  • theopenstudyowl
Math graphing help. Medals.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
theopenstudyowl
  • theopenstudyowl
theopenstudyowl
  • theopenstudyowl
Its #4 only
theopenstudyowl
  • theopenstudyowl
Anything?

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More answers

jim_thompson5910
  • 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
  • theopenstudyowl
@ (-2,1) and (2,2)
theopenstudyowl
  • theopenstudyowl
oh wait, sorry those are the points of intersection of the two functions, one sec.
theopenstudyowl
  • theopenstudyowl
at x=3
jim_thompson5910
  • jim_thompson5910
see attached
1 Attachment
theopenstudyowl
  • theopenstudyowl
does this have to do with the vertical line test?
jim_thompson5910
  • jim_thompson5910
no, I'm simply asking for the value of f(-4)
theopenstudyowl
  • theopenstudyowl
oh
theopenstudyowl
  • theopenstudyowl
Ok, could you help me with the domain and range part of the problem please.?
jim_thompson5910
  • jim_thompson5910
so you figured out that part already? the f(-4) part?
theopenstudyowl
  • 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
  • jim_thompson5910
I see
jim_thompson5910
  • jim_thompson5910
the domain is the set of allowed inputs, in other words, the set of allowed x values
theopenstudyowl
  • theopenstudyowl
ok...
jim_thompson5910
  • 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
  • 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
  • jim_thompson5910
what would be the domain of g(x) ?
theopenstudyowl
  • theopenstudyowl
ok, I'll solve that now, could you explain to me when I include brackets and parenthesis when writing these things..?
theopenstudyowl
  • theopenstudyowl
The domain of g(x) is [-4,3]
jim_thompson5910
  • 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
  • jim_thompson5910
|dw:1440727856238:dw|
jim_thompson5910
  • 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
  • theopenstudyowl
So when there is a circle, I use brackets?
theopenstudyowl
  • theopenstudyowl
oh wait parenthesis nvm
jim_thompson5910
  • jim_thompson5910
|dw:1440728130377:dw|
theopenstudyowl
  • theopenstudyowl
ok thanks, could you help me with the range too plz?
jim_thompson5910
  • 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
  • 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
  • theopenstudyowl
ok, is my domain for g(x) correct?
jim_thompson5910
  • jim_thompson5910
what did you say for the domain of g(x)?
jim_thompson5910
  • jim_thompson5910
oh nvm, you wrote `The domain of g(x) is [-4,3]`
jim_thompson5910
  • jim_thompson5910
yeah that is correct
theopenstudyowl
  • theopenstudyowl
yah!
theopenstudyowl
  • theopenstudyowl
ok, give me a sec for the other one...
theopenstudyowl
  • theopenstudyowl
1/2 is less than or equal to y is less than or equal to 4
jim_thompson5910
  • jim_thompson5910
I don't agree with the 1/2 part
jim_thompson5910
  • jim_thompson5910
oh wait, nvm
jim_thompson5910
  • jim_thompson5910
each tick is 1
theopenstudyowl
  • theopenstudyowl
its hard to tell
jim_thompson5910
  • jim_thompson5910
1/2 is a good estimate
jim_thompson5910
  • jim_thompson5910
what would the range be in interval notation?
theopenstudyowl
  • theopenstudyowl
[1/2,4]
theopenstudyowl
  • theopenstudyowl
?
jim_thompson5910
  • jim_thompson5910
correct
theopenstudyowl
  • 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
  • jim_thompson5910
it depends on if you have open or closed circles |dw:1440728925694:dw|
jim_thompson5910
  • jim_thompson5910
when you include a point, you say "or equal to" eg: \[\Large x \le 5\] we're including 5
jim_thompson5910
  • jim_thompson5910
saying `x > 5` we mean everything larger than 5 and we exclude 5 from the set
theopenstudyowl
  • theopenstudyowl
ok cool, thanks!
jim_thompson5910
  • jim_thompson5910
sure thing
theopenstudyowl
  • theopenstudyowl
http://assets.openstudy.com/updates/attachments/55dfbcb4e4b0819646d75855-theopenstudyowl-1440726228078-unnamed.jpg http://assets.openstudy.com/updates/attachments/55dfbcb4e4b0819646d75855-theopenstudyowl-1440726228718-unnamed1.jpg
theopenstudyowl
  • 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
  • theopenstudyowl
@jim_thompson5910 does anything look incorrect?
jim_thompson5910
  • jim_thompson5910
`c) An estimation of the solution of the equation f(x)=-1, is x=3.` there's one other solution
theopenstudyowl
  • theopenstudyowl
ok
jim_thompson5910
  • 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
  • theopenstudyowl
ok cool, does everything else look ok?
jim_thompson5910
  • jim_thompson5910
everything else is perfect
theopenstudyowl
  • theopenstudyowl
ok, and for c, how would I find that other point?
jim_thompson5910
  • jim_thompson5910
draw a horizontal line through y = -1 and see where it crosses the red f(x) function
jim_thompson5910
  • jim_thompson5910
you already found (3,-1)
jim_thompson5910
  • jim_thompson5910
actually I think you meant to say (-3,-1)
jim_thompson5910
  • jim_thompson5910
if f(x) = -1, then x = -3 or x = ???
theopenstudyowl
  • theopenstudyowl
one sec
theopenstudyowl
  • theopenstudyowl
and 4?
jim_thompson5910
  • jim_thompson5910
yep
theopenstudyowl
  • theopenstudyowl
so its x=-3 and 4?
jim_thompson5910
  • jim_thompson5910
yes if f(x) = -1, then x = -3 or x = 4
theopenstudyowl
  • 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
  • jim_thompson5910
glad to be of help

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