I've been doing revision for yearlies and I've been having difficulties figuring out these questions:
1) Sketch the graph of the periodic function such that f(x) = x for – 1 < x ≤ 1 where the period of f(x) is 2.
2) Find the largest possible domain and range of the function f(t) = abs(t) – t.
3) If f(x) = x^2 – 6x + 5, sketch a graph of the region defined by the intersection of the inequalities f(x) + f(y) ≤ 0 and f(x) – f(y) ≥ 0.
Could you please help me out?
The first two are very straightforward. The third - I'm still thinking about!
Originally Posted by xwrathbringerx
(1) Between -1 and 1, the graph is the line y = x; i.e. at 45 degrees to the axes between (-1,-1) and (1, 1), excluding (-1, -1), but including (1, 1). This covers a range of values of x of length 2, the period of the function. So this line segment is repeated between x = 1 and x = 3, and again, and again, ... Also to the left between x = -3 and x = -1, etc... See sketch.
(2) Assuming is real, the domain is all the real numbers.
If which is for .
So the range is all the non-negative reals.
Hmmmm perhaps I have to shade the regions f(x) ≤ - f(y) and f(x) ≥ f(y)</SPAN>
BUT I have no idea what the final image should look like (like the final areas shaded)
Could you please show me?