Symmetric to the x-axis, y-axis or origin

[jhawk555]

I understood this when we went over it in class, but I can't remember how to figure this out.

y-axis: (x,y) then (-x,y)
x-axis: (x,y) then (x,-y)
origin: (x,y) then (-x,-y)


Is the following symmetric to the x-axis, y-axis or origin?
y=4x^3-6x

To figure this out I follow the above rules.

Origin: -y=-4x^3- (-6x) Multiply by -1
(-1)-y=(-1)-4x^3-(-6x)
y=4x^3-6x
{Answer: Yes}

y-axis: y=-4x^3 - (-6x) {Answer: No}

x-axis: -y=4x^3-6x {Answer: No}

Did I do this correctly?

 

[tkhunny]

I understood this when we went over it in class, but I can't remember how to figure this out.

y-axis: (x,y) then (-x,y)
x-axis: (x,y) then (x,-y)
origin: (x,y) then (-x,-y)


Is the following symmetric to the x-axis, y-axis or origin?
y=4x^3-6x

To figure this out I follow the above rules.

Origin: -y=-4x^3- (-6x) Multiply by -1
(-1)-y=(-1)-4x^3-(-6x)
y=4x^3-6x
{Answer: Yes}

y-axis: y=-4x^3 - (-6x) {Answer: No}

x-axis: -y=4x^3-6x {Answer: No}

Did I do this correctly?

Your language is a bit difficult to follow, but it looks like you are heading in the right direction.

"(x,y) then (-x,y)" That doesn't actually mean anything. Use function notation or more verbiage to explai what you mean. f(x,y) = f(-x,y), for example.

"y-axis: y=-4x^3 - (-6x) {Answer: No}" That's a nice enough answer, but you have not explained what you were thinking that caused you to formulate that opinion.

So, ...just upgrade your reporting skills a little. It will save you later.