Question

Help please
Is this function below is symmetric to the x-axis, y-axis, orign, or has has no symmetry at all.

Answer 1

y = - 4x ^3

Answer 2

@ganeshie8

Answer 3

http://www.mathsisfun.com/algebra/equation-symmetry.html

Answer 4

\(\large f(-x) = -4(-x)^3 = 4x^3 \ne f(x)\)
so the function is NOT symmetric about `y` axis

Answer 5

still we need to check whether it is symmetric about x axis or origin..

Answer 6

know how to check them ?

Answer 7

no

Answer 8

To check symmetry about x axis :
replace `y` with `-y`

if the function does not change, then it is symmetrical about x axis

Answer 9

\(\large y = -4x^3\)

replace `y` by `-y`, you get :
\(\large -y = -4x^3 \)

\(\large \implies y = 4x^3 \ne f(x)\)

So the function is NOT symmetric about x axis also

Answer 10

ok what would be

Answer 11

are we done with the first question ? :)

Answer 12

we still need to check if it has symmetry about `origin` right ?

Answer 13

oh yea sorry

Answer 14

its okay... try below for testing symmetry about `origin` :

y = - 4x ^3

replace `x with -x` and `y with -y`

if the function does not change, then it is symmetrical about `origin`

Answer 15

y = - 4x ^3

replace `x with -x` and `y with -y`

what do u get ?

Answer 16

what do i look for i dont understand

Answer 17

y = -4x^3

replace x with -x and y with -y

you get :
-y = -4(-x)^3

Answer 18

if you simplify, you will see that its exactly same as the original function :

-y = -4(-x)^3
-y = 4x^3
y = -4x^3

So the function is symmetric about the origin

Answer 19

if that makes more or less sense...