confusing graphs question (1 Viewer)

[bally24]

in fitz exercise 30a it asks you to graph y=sqrt ((cosx - 1)²) Can't you simplify this to y=cosx - 1 and graph that? But when I graphed it on my graphing program, I was wrong. I know Im missing something but I'm starting to get really confused about it - could someone clarify this for me? (my half yearly's tomorrow :worried

Heres the graphs of y=sqrt ((cosx - 1)²), y=((cosx - 1)²) and y=cosx - 1.

 

[pLuvia]

y=sqrt[(cosx-1)²] does not equal to y=cosx-1
y=sqrt[x²]=y=|x| that means your graph should be y=|cosx-1|

Hope that helped

 

[Riviet]

Remember that sqrt[f(x)] is always positive and is undefined when f(x)<0. Using what pLuvia said that sqrt{f(x)²}=|f(x)|, the graph of y=|f(x)| is basically the graph of y=f(x), except with the parts of the graph below the x-axis reflected in the x-axis (since f(x) < / 0).

 

[bally24]

oh right, i tmakes more sense when i think about it in terms of y=sqrt x^2 instead of all this trig, thanks for your help guys