Question

If the graph of an equation is symmetric with respect to the origin and (3,-4) is a point on the graph then what is also a point on the graph?

Answer 1

Do you know what it means for a function to be symmetric wrt to the origin? What does that mean, algebraically?

Answer 2

^exactly what does it mean?

Answer 3

If a function f(x) is symm wrt the origin, it means that:

\[\large f(-x)=-f(x)\]for all x in the domain of f(x)

Answer 4

An example would be \(\large f(x)=x^3\), since for any x, if I compare the y value at x and the y value at -x, they are opposites. E.g.

\(\large f(2)=8\) and \(\large f(-2)=-8\)

So can you take that definition, and relate it to what it means regarding the point given above?

Answer 5

What about the y coordinate then?

Answer 6

Huh? y=f(x)

f(x) IS the y-coordinate. Every point on the graph is (x, f(x))

Answer 7

Good luck

Answer 8

In the cubic example I gave above, the 2 points are (2,8) and (-2,-8)

Answer 9

So then for it to be symmetric with respect to the origin would the point be (-3,4)?

Answer 10

one example as my teacher gave which i liked is the ying yang sign - can be rotated 180 degrees is the symmetric with respect to the origin

Answer 11

do you see?

Answer 12

yes I do! that helped so much I thought that's what it was! thank you so much!

Answer 13

:) taking precalculus now so glad i could help :)

Answer 14

it was a ton of help! good luck with that :))

Answer 15

Yes, (-3,4), you got it! :)

Answer 16

yay! :)

Answer 17

does anyone know the intercepts to
y=5x^2-5

Answer 18

to find the x and y intercepts set y=0 then solve for x then set x to 0 and solve for y

Answer 19

I got that one too! thank you again! :)