Write a rule for a function whose graph is the graph of c(x)= cos (x) reflected across the x-axis and...?

... and translated up 1 unit. How does the amplitude and period of this new function compare to those of c(x)= cos (x)? Why does this make sense?





Ok, the bit about reflecting across the x-axis- reflect how? Seeing as how the sinusoidal graph is on the x-axis I'm not sure which direction to reflect it. Otherwise, I can do the problem. So if anyone clarify that part for me, I can just take it from there.

Write a rule for a function whose graph is the graph of c(x)= cos (x) reflected across the x-axis and...?
This is the original formula


y=cos(x)





To reflect on x axis, meaning flip it over in this case, as the graph is already on x axis. y=1 becomes y=-1 and 0 remains 0. it becomes


y=-cos(x)





To translate up 1 unit, add 1, it becomes


y=-cos(x)+1
Reply:Reflecting cos x across the x-axis causes a 180 degree phase shift. Otherwise, it changes nothing.





Translating the reflection up one unit causes one to be added to everyy point of the reflection, so that the max value is now 2 and the min value is now zero.





The amplitude and the period remain the same.


To alter the amplitude you would have to multiply cos x by some number such as 10. To alter the period you would have to multiply x by some constant. Neither of those things was done by the reflection and the translation.

imperial