Compare the functions shown below: (picture below) Which function has the greatest y-intercept?

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Compare the functions shown below: (picture below) Which function has the greatest y-intercept?

Mathematics
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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
I understand, but how do you get the function from the middle graph?

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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?
I got -5 and 7.13 for the other two... and I'm not sure which is smaller...
I mean I know what's smaller between -5 and 7.13 - but not cosine or sine
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.
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
Well it's one number off this time
note that $$ \cos -\pi = \cos \pi=-1 $$
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...
$$ 0-\pi = -\pi $$ right?
I didn't think that would be correct...
Well I just tested it on my calculator and that's true, I never knew that occurred.
|dw:1433628863181:dw|
|dw:1433629021890:dw|
OH MY GOSH I FEEL SO STUPID I COULD GET THE Y INTERCEPT FROM THE MIDDLE BY JUST LOOKING AT THE GRAPH /)-_-
Oh I see whatcha did there!
|dw:1433629149771:dw|
Yes, if you want the y-intercept, look at the graph where x=0, that's where the graph "intercepts" the y-axis
|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!
I appreciate this so much.
no problem - so do you need more help with this one?
yes please, let me try to redo the middle one and I'd like for you to check it
Great!
Would it be -3?
The y-intercept of the middle graph is -3. Yes!
Yay!
Thank you Chris Evans guy!
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
I was just trying to figure out what the greatest y intercept was, but I had questions within the question which you answered
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..
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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)?
Did we not just do all of that??
What did you get for f(0),g(0) and h(0)?
Doesn't f(0) mean that you set the x to 0 in the function? That's exactly what we did!
Yes, so f(0) was what?
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.
Oh, the last one was the one you corrected me on and I redid, I'll do it again then.
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...
oh right the cos and pi thing
?
$$ h(0) = 2 \cos(2\times0 − \pi) + 4\\ h(0) = 2 \cos(−\pi) + 4\\ h(0) = 2\times \color{red}{-1} + 4\\ h(0) = -2+4\\ $$ http://www.wolframalpha.com/input/?i=cos%28-pi%29
So that leaves me with -2, and that's the greatest value!
-2+4=2
Herp a derp, I knew that >.<
Thank you so much!
yep, so f(0)=-5 g(0)=-3 h(0)=2 The order from smallest to largest: -5<-3<2
yay!
good job :)
Why thank you Mr. Evans.

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