Question

I need some help on my homework: Transformations of Functions! If you could help me, and answer a couple of questions, that'd be great!

Answer 1

My first question is that I am given the function \(\ \huge y=x^2 \). How would I write the equation for a reflection across the origin?

Answer 2

I know that this equation illustrates a parabola

Answer 3

this is how is look the y=x^2

Answer 4

Reflection over the origin is represented as the transformation \[(x, y) \rightarrow (-x, -y)\]
So to reflect \[y = x^{2}\] over the origin, you would insert \[-y\] and \[-x\]into the equation, and then solve for \[y\]

Answer 5

that seem to be good

Answer 6

So you get \(\ \huge -y=-x^2 ? \) That can't be right...

Answer 7

@Andresfon12 How can you tell that this function is not a parabola? i thought this was the parent function of a parabola?

Answer 8

Well, when you plug -x in for x in \[y = x^{2}\] remember that x is squared, leading to a positive \[x^2\] value regardless of whether or not x is actually positive.

Answer 9

I thought you said to plug in -y and a -x into the equation?

Answer 10

i just poster how is look the y=x^2 in the graph

Answer 11

Sorry, I wasn't being clear. I meant to plug -y and -x in for y and x in your equation. Your result should be \[-y = (-x)^{2}\]

Answer 12

just use x=1,2,3,4 which y=1,4,9,16,25

Answer 13

So the equation for this function when reflected across the origin is \(\ \huge -y=x^2?\). Is \(\ \huge y=-x^2\) the same thing?

Answer 14

thepotato is right

Answer 15

So this is an exponential function? How does the function of a parabola look then?

Answer 16

Yeah, that answer's right.

Answer 17

Wait, exponential function? This is a parabola

Answer 18

Sorry about the squiggly line, pretend that's a smooth curve

Answer 19

that graph almost look the same as my

Answer 20

bad draw here too

Answer 21

What about the other half?