anonymous
  • anonymous
The function f (x) = x^4 has an axis of symmetry the vertical axis y. True or False? This is true right??
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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wolfe8
  • wolfe8
I forgot how to check this, but I think you need to find where the gradient is = 0.
anonymous
  • anonymous
One way to check is of course to plot the given function. You'll see it has an axis of symmetry at y-axis. Another way is to replace x with -x. If the resulting function is the same as the original, it has an axis of symmetry at the y-axis. Like, in the given function, f(x) = x^4 f(-x) = (-x)^4 f(-x) = x^4 = f(x) i think so...
jdoe0001
  • jdoe0001
yeap

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anonymous
  • anonymous
do you agree?
jdoe0001
  • jdoe0001
yes, you're correct on the check for f(-x) and you're also correct on checking the graph too, mind you that for any function of that kind with a EVEN exponent, y-axis is always their line of symmetry
anonymous
  • anonymous
what about this one? In the values interval [0, 2p] the function f (x) = sin(x) has more periods by the function g (x) = sin(3x). True or False?
anonymous
  • anonymous
i thought that was true but...i am not sure... now i believethat is false!!
jdoe0001
  • jdoe0001
\(\bf sin(Bx) \textit{ period is } \cfrac{\textit{regular period of sine}}{B} \implies \cfrac{2\pi}{B}\\ sin(3x) \textit{ period is }\cfrac{2\pi}{3}\)
jdoe0001
  • jdoe0001
so, sin(x) regular period is \(\bf 2\pi\) sin(3x) has \(\bf \cfrac{2\pi}{3}\) so 2/3 of a pi, one period 4/3 of a pi, 2 periods 6/3 of a pi, 3 periods notice that 6/3 = 2, that is \(\bf 2\pi\) so sin(3x) has 3 times the periods as sin(x)
anonymous
  • anonymous
so you say that is true?
jdoe0001
  • jdoe0001
well, notice, sin(3x) has 3 periods between 0 and \(2\pi\) sin(x) only has one, same interval
anonymous
  • anonymous
yes so its true...
anonymous
  • anonymous
oh...is the opposite...what i am thinking??? ahaha./.. it is false!!
jdoe0001
  • jdoe0001
well, it says "has more periods by the function g(x)" it doesn't say "has more periods THAN the function g(x)"
jdoe0001
  • jdoe0001
does sin(x) has more periods than sin(3x)? no does sin(x) has more periods if it were rewritten as sin(3x)? yes
anonymous
  • anonymous
oh pellet... one word ... ....by...... means than the first has fewer from second?
anonymous
  • anonymous
i am not fluent in english
jdoe0001
  • jdoe0001
well, I guess we dunno what they mean... can you post a screenshot of it?
anonymous
  • anonymous
hahaha it is not in english,,, ket me see my translation again it was my mistake..
anonymous
  • anonymous
i used gogle translator... oh...
anonymous
  • anonymous
the correct translation is : f(x) has more periods THAN the function g(x)
anonymous
  • anonymous
so is False
jdoe0001
  • jdoe0001
ohh, then is false :)
anonymous
  • anonymous
just tell me... can i use ....by... when?
anonymous
  • anonymous
for example 4 is bigger by 3?? can i say this?
anonymous
  • anonymous
it asks if 3 is bigger than 4 but stating"is 4 bigger by 3??"
anonymous
  • anonymous
btw they are both correct thank you!
jdoe0001
  • jdoe0001
"by" denotes a relationship of dependency something by something else, means something is affected by something else "than" denotes comparison something than something else, means something in comparison to something else
jdoe0001
  • jdoe0001
yw
anonymous
  • anonymous
yes i know for "than"
anonymous
  • anonymous
i did not know about by
anonymous
  • anonymous
so i have to join this site whenever i have time to improve my english ahahaha
jdoe0001
  • jdoe0001
hehehe

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