Question

The function f (x) = x^4 has an axis of symmetry the vertical axis y.

True or False?

This is true right??

Answer 1

I forgot how to check this, but I think you need to find where the gradient is = 0.

Answer 2

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...

Answer 3

yeap

Answer 4

do you agree?

Answer 5

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

Answer 6

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?

Answer 7

i thought that was true but...i am not sure... now i believethat is false!!

Answer 8

\(\bf sin(Bx) \textit{ period is } \cfrac{\textit{regular period of sine}}{B} \implies \cfrac{2\pi}{B}\\
sin(3x) \textit{ period is }\cfrac{2\pi}{3}\)

Answer 9

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)

Answer 10

so you say that is true?

Answer 11

well, notice, sin(3x) has 3 periods between 0 and \(2\pi\)
sin(x) only has one, same interval

Answer 12

yes so its true...

Answer 13

oh...is the opposite...what i am thinking??? ahaha./.. it is false!!

Answer 14

well, it says "has more periods by the function g(x)"
it doesn't say "has more periods THAN the function g(x)"

Answer 15

does sin(x) has more periods than sin(3x)? no
does sin(x) has more periods if it were rewritten as sin(3x)? yes

Answer 16

oh pellet... one word ... ....by...... means than the first has fewer from second?

Answer 17

i am not fluent in english

Answer 18

well, I guess we dunno what they mean... can you post a screenshot of it?

Answer 19

hahaha it is not in english,,, ket me see my translation again it was my mistake..

Answer 20

i used gogle translator... oh...

Answer 21

the correct translation is : f(x) has more periods THAN the function g(x)

Answer 22

so is False

Answer 23

ohh, then is false :)

Answer 24

just tell me... can i use ....by... when?

Answer 25

for example 4 is bigger by 3?? can i say this?

Answer 26

it asks if 3 is bigger than 4 but stating"is 4 bigger by 3??"

Answer 27

btw they are both correct thank you!

Answer 28

"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

Answer 29

yw

Answer 30

yes i know for "than"

Answer 31

i did not know about by

Answer 32

so i have to join this site whenever i have time to improve my english ahahaha

Answer 33

hehehe