Question

Reflecting the graph y=sin x across the y-axis is the same as reflecting it across the x-axis.

True or False.

I think it would be true because it you rotated the graph it would still match up.

Please explain. Thank you!

Answer 1

What do you do to a function to reflect across the x-axis? and the y-axis?

Answer 2

y = f(x)
f(-x) reflects it across y-axis.
-f(x) reflects it across x-axis.

Answer 3

So mathematically you'd need to do different things to the graph to reflect it either the x or the y, I think the results are the same though.

Answer 4

y = sin(x) --- (1)
y = sin(-x) reflects it across y-axis. --- (2)
y = -sin(x) reflects it across x-axis. --- (3)

Since sin(-x) = -sin(x), operations (2) and (3) have the same effect.