chaotic_butterflies
  • chaotic_butterflies
Compare the functions shown below: (picture below) Which function has the greatest y-intercept?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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chaotic_butterflies
  • chaotic_butterflies
@iambatman
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ybarrap
  • ybarrap
Set x= to zero and compare value of the two functions. When you set x=0, the function is crossing the y-axis - hence the term, "y-intercept." Recall that cos(0) = 1 and cos(0 - pi) = cos (-pi) = -1
chaotic_butterflies
  • chaotic_butterflies
I understand, but how do you get the function from the middle graph?

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chaotic_butterflies
  • chaotic_butterflies
@ybarrap
ybarrap
  • ybarrap
If you want to find the function that matches the middle graph you need to first determine for this function, whether you are going to use cosine or sine. Which function, cosine or sine, is smaller at x=0?
chaotic_butterflies
  • chaotic_butterflies
I got -5 and 7.13 for the other two... and I'm not sure which is smaller...
chaotic_butterflies
  • chaotic_butterflies
I mean I know what's smaller between -5 and 7.13 - but not cosine or sine
ybarrap
  • ybarrap
Which of these is similar to the function in your middle graph: |dw:1433628050735:dw| To determine which is small between -5 and 7.13 use the number line |dw:1433628325169:dw| I don't know how you got 7.13 from the second function.
chaotic_butterflies
  • chaotic_butterflies
I'm thinking sine... and I'll explain. h(x) = 2 cos(2x − π) + 4 h(x) = 2 cos(0 − π) + 4 h(x) = 2 cos(π) + 4 h(x) = 2 cos(π) + 4 h(x) = 0.99..(3.14) + 4 h(x) = 4.13 + 4 h(x) = 8.13
chaotic_butterflies
  • chaotic_butterflies
Well it's one number off this time
ybarrap
  • ybarrap
note that $$ \cos -\pi = \cos \pi=-1 $$
chaotic_butterflies
  • chaotic_butterflies
but would it be negative pi because it's just being subtracted from 0 which is nothing - so if you take nothing away from something, that doesn't alter it...
ybarrap
  • ybarrap
$$ 0-\pi = -\pi $$ right?
chaotic_butterflies
  • chaotic_butterflies
I didn't think that would be correct...
chaotic_butterflies
  • chaotic_butterflies
Well I just tested it on my calculator and that's true, I never knew that occurred.
ybarrap
  • ybarrap
|dw:1433628863181:dw|
ybarrap
  • ybarrap
|dw:1433629021890:dw|
chaotic_butterflies
  • chaotic_butterflies
OH MY GOSH I FEEL SO STUPID I COULD GET THE Y INTERCEPT FROM THE MIDDLE BY JUST LOOKING AT THE GRAPH /)-_-
chaotic_butterflies
  • chaotic_butterflies
Oh I see whatcha did there!
ybarrap
  • ybarrap
|dw:1433629149771:dw|
ybarrap
  • ybarrap
Yes, if you want the y-intercept, look at the graph where x=0, that's where the graph "intercepts" the y-axis
ybarrap
  • ybarrap
|dw:1433629403543:dw| See how one is rotating counter clockwise and the other is rotating clockwise by 180 degrees but in the end, both are facing YOU!
chaotic_butterflies
  • chaotic_butterflies
I appreciate this so much.
ybarrap
  • ybarrap
no problem - so do you need more help with this one?
chaotic_butterflies
  • chaotic_butterflies
yes please, let me try to redo the middle one and I'd like for you to check it
ybarrap
  • ybarrap
Great!
chaotic_butterflies
  • chaotic_butterflies
Would it be -3?
ybarrap
  • ybarrap
The y-intercept of the middle graph is -3. Yes!
chaotic_butterflies
  • chaotic_butterflies
Yay!
chaotic_butterflies
  • chaotic_butterflies
Thank you Chris Evans guy!
ybarrap
  • ybarrap
There seems to be a few things you've asked here: y-intercept, graph of the function, which function has biggest y-intercept. Not sure which you are solving. brb
chaotic_butterflies
  • chaotic_butterflies
I was just trying to figure out what the greatest y intercept was, but I had questions within the question which you answered
chaotic_butterflies
  • chaotic_butterflies
But wait, my options don't allow me to pick both g(x) and h(x), yet they both have the same y intercept which is larger than -5..
chaotic_butterflies
  • chaotic_butterflies
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ybarrap
  • ybarrap
Ok, now I see the whole problem now, LOL It's asking which functions, f(x), g(x) , h(x) or all have the greatest y-intercept (i.e. which has the largest value of y when x=0): $$ f(0)\\ g(0)\\ h(0) $$ What is f(0)? What is g(0)? What is h(0)?
chaotic_butterflies
  • chaotic_butterflies
Did we not just do all of that??
ybarrap
  • ybarrap
What did you get for f(0),g(0) and h(0)?
chaotic_butterflies
  • chaotic_butterflies
Doesn't f(0) mean that you set the x to 0 in the function? That's exactly what we did!
ybarrap
  • ybarrap
Yes, so f(0) was what?
ybarrap
  • ybarrap
I see that you've highlighted f(0)=-5,g(0)=-3 and maybe h(0)=-3. The last one is not correct. Once you get all these right, compare them and take the max.
chaotic_butterflies
  • chaotic_butterflies
Oh, the last one was the one you corrected me on and I redid, I'll do it again then.
chaotic_butterflies
  • chaotic_butterflies
h(x) = 2 cos(2x − π) + 4 h(x) = 2 cos(− π) + 4 h(x) = - 3.13 + 4 h(x) = 0.86 Oh wow that's wayy different...
chaotic_butterflies
  • chaotic_butterflies
oh right the cos and pi thing
chaotic_butterflies
  • chaotic_butterflies
?
ybarrap
  • ybarrap
$$ h(0) = 2 \cos(2\times0 − \pi) + 4\\ h(0) = 2 \cos(−\pi) + 4\\ h(0) = 2\times \color{red}{-1} + 4\\ h(0) = -2+4\\ $$ http://www.wolframalpha.com/input/?i=cos%28-pi%29
chaotic_butterflies
  • chaotic_butterflies
So that leaves me with -2, and that's the greatest value!
ybarrap
  • ybarrap
-2+4=2
chaotic_butterflies
  • chaotic_butterflies
Herp a derp, I knew that >.<
chaotic_butterflies
  • chaotic_butterflies
Thank you so much!
ybarrap
  • ybarrap
yep, so f(0)=-5 g(0)=-3 h(0)=2 The order from smallest to largest: -5<-3<2
chaotic_butterflies
  • chaotic_butterflies
yay!
ybarrap
  • ybarrap
good job :)
chaotic_butterflies
  • chaotic_butterflies
Why thank you Mr. Evans.

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