Another Curve Sketching question

Hi, sorry to post another question about curve sketching (this is my last one) but I am having difficulties with the following function:

f(x) = cosx - sinx

If someone could provide a sketch of what this function looks like that would be great, that way I have something to work towards. I've done all the calculus work but I'm having a real hard time making sense of it.

I have:

- the y-int: y=1

- the zeros: x=(pi)/4 and 5(pi)/4

- niether odd or even

- no asymptotes

- increasing everywhere (I'm really not sure if that is right)

- no local max/min

- concave down everywhere (I'm also not sure if that is right)

- no inflection points

I've had no luck graphing this so I'm sure I've made a big mistake somewhere. Any help at all would be great!

Thanks.